Huh... welp, guess I might as well say something right? Sure.
5. To make sure we have our bases covered, is Fairy Lock a move we want to explore in any capacity? Is it viable at all? Why or why not?
I'll give this a quick run down.
Yes, I believe we should explore Fairy Lock in
some capacity, as it does have a few niche uses, which could be pulled into maybe one or two sets on TrapCAP.
However, I do NOT believe that Fairy Lock should be our main trapping move. I'm personally not sure why people have got it into their heads that TrapCAP cannot run two types of trapping moves to achieve different effects, as I don't recall an only-one-trap-move clause being instituted by anyone running the thread or by the concept itself (maybe I'm blind though, who knows?). Personally, I would even go so far as to say limiting TrapCAP to only one type of trap move would be detrimental to the project. Is it not more beneficial (as someone else mentioned earlier) to TrapCAP's viability if it can run different styles of trapping sets to increase its unpredictability, helping make the trap moves in and of themselves a bit more useable?
Regardless, I digress, back to Fairy Lock. As for whether it is viable or not, I feel that it has most definitely been undersold here. Yes, it only provides one turn of trapping and also traps the user, those can be certainly considered as downsides in some capacity. BUT, as people here have already pointed out, there are very effective ways to use it. I personally am very intrigued by the Eject Button concept earlier, as it allows for a new Mon to come in and potentially OHKO the trapped opponent mon, not once in a battle, but twice if the eject button goes off properly and ALSO when TrapCAP is killed off later in the battle. It has two chances to greatly benefit its team by ensuring OTHER POKEMON can land their Super Effective Super Critical Z Move Power moves or what have you. In addition, consider that Fairy Lock can achieve a similar theme as other trapping moves when run as a pivoting set. Fairy Lock whatever comes in to screw with TrapCAP if you're able to, then VoltTurn out to a solid check/counter (granted this requires speediness, which may be poll jumping a bit) before the opponent attacks, potentially reversing the pressure dynamic of the situation. Imagine being able to send in Specs Analytic Volkraken in some version of this scenario. That's a free shot at pretty much anything with those super potent moves.
Long story short, I think Fairy Lock has potential in a few sets, and should be at least tangentially explored if possible, as is consistent with the project's goal of exploring trapping mechanics. Though I do NOT believe it should be the main trapping move TrapCAP can utilize. By extension, I don't believe TrapCAP should be limited to only one trap move in general, for the sake of potential unpredictability and thereby viability.
6. Should we focus more on the binding move + residual damage / stall strategy for CAP23? Or, should we focus on the offensive strategy using primarily Anchor Shot and Spirit Shackle as well as binding moves alongside Z-moves, pivot moves, etc.? Why is one better than the other?
Allow me to tweak this answer a bit for my own tastes. I am not necessarily as much
FOR an offensive strategy as I am
AGAINST a stalling strategy. As has been pointed out previously in the thread, a more defensive style of trapper takes time to establish its dominance in the battle. First it has to trap. Then it has to Toxic. By then it probably has to heal up, and if we were to make it bulky enough that it doesn't need to, then that's just a whole different set of problems (such as why bother using the trapping moves instead of just using it as a defensive pivot or tank or wall). After that though, then maybe you start attacking with something, by which point the five turns of a binding move are almost up (If binding band is in use, then you lack an item slot, giving up leftovers, necessitating the use of a healing move to maintain relevance, ergo taking up more turns of the trap effect by healing, lessening stall potential, etc.). Generically, I see defensive trapping as too straightforward to be viable. Consider the only currently relevant mon who can use it: Heatran. The reason that trapping effect is so potent is because it's usually unexpected. The viability of the mon via other sets makes trapping unexpected, encouraging the opponent to make plays that lead to traps and potent stalling. Now, if TrapCAP were to focus solely on defensive trapping, the linearity would make it unviable simply by its one-track nature, or we'd have to make other sets for it that also work that aren't stall-traps to increase its unpredictability. What would these other sets be? They can't be other defensive trapping moves, as that still makes the sets linear, which necessitates either offensive or supportive trapping (which would likely prove difficult due to stat distribution), or ignoring trapping sets at all. In essence, from my point of view, defensive and stall-based trapping is limiting to the idea of exploring trapping moves, as the methodology is already fairly well known and such a build could result in set linearity and as a result reduced viability. For this reason, I particularly prefer an either offensive or supportive style of TrapCAP that is able to control switching to its own advantage or to aid in predictions for other Pokémon on its team. That is where I see most of the explorability and potential in trapping.
Also, since Hesh's post came up while I was still drafting this, I'm gonna go through some of the problems I see with defensive trapping from his point of view as well.
Run a defensive one, and you've got free selection of what Trapping Move to run; doesn't matter if Bind only does 10BP and has no STAB (or even if it did, so what? It's now 15BP wooo). Give it a Grip Claw, and it does 87.5% damage guaranteed over 7 turns (or Binding Band to do a guaranteed 67% damage over 4 turns)
This is fundamentally subversive in how it addresses trapping moves. Technically offensive move pairings can be done with any trapping move as well, there is no "Only-one-trapping-move" limit, as I previously stated. It simply happens to be that AS and SS happen to be very good for those strategies. The same can be said about defensive, AS and SS are far better for stalling set ups than binding moves, as they prevent all hope of escape for mons caught and without Ghost typing or pivot moves, allowing a guaranteed kill through Toxic or whatever you're doing. This cannot be said about binding moves, which allow the opponent to escape to a possible cleric or better suited mon to handle the defensive strat after a few turns. The argument that offensive limits move choice is about as logical as saying defensive options limit move choice, because it's the SAME SITUATION. You could choose other moves, but some moves are just better for your strategy. There are ways to work with both, (and I personally believe that lies in a middle supportive-offense stance).
Do you make it bulky by debuff or selfbuff? What type do you run? Ghost, to give immunity to mirror match trap? Do you want it to counter Shed Shell/Leftovers and give it Knock Off, and do you want that Knock Off to be a damage dealer? Do you want to make Toxic+Trap a thing against all mon? Then suggest Corrosion or Normalize (except for Pesky Ghosts, but they're pretty hard counter to the concept in any case). Alternatively, what other Chip Damage is there; Sandstorm/Hail/Will O Wisp/Ghost Curse. Do you want to punish switchers? Suggest Stakeout/Pursuit. Do you want it to be something that can put momentum back in your court by forcing an opponent to stop you doing X to be a force multiplier such as by being a Cleric, or have it be able to boost its offense; is it worthwhile suggesting Slow Start for an ability? Do you want to be a Stat Cleaner/resetter? Do you want to build up offense by using "ramp up" moves like Fury Cutter/Ice Ball/Roll Out, and is it worthwhile supporting those moves to let them "set up" against a mon effectively until it's at ridiculous levels; for example, using a Metronome with a Fury Cutter is going to give a flat +40% boost to its 160BP.
Again, the same can be said for an offensive role. Defense has many options, sure, but they can't all be run conjointly. You can't have both Stakeout AND Corrosion. You eventually have to pick one. The essence of the sets all comes to the same source: passive damage building up due to trapping. Allow me to stress this idea. Variations on a theme ARE NOT different themes. Offensive has options as well. Do we want a fast Z move attacker? A bulky set-up sweeper? A fast set-up sweeper? A coverage demon? A STAB Spammer? A switch punisher? These are all variants on an offensive style each targeting different aspects of offense. In the same way, different styles of build-up damage do not change the problem of build-up/debuff strategies, being that they take a while to set up. When using trap MOVES, which have already been established to have a 'weakness' in allowing the opponent to switch in a good check, the slow-to-effectiveness issue of defensive trapping is further amplified, bringing into question whether it's a the optimal way to approach trapping as a whole.
The risk from being offensive is that it ends up no different from any other offensive mon, or has the "gimmick" of having to use a Trapping move to complete its task (which it's even less capable at, because it's having to play around with 4MSS when one slot is already taken).
I think you're misunderstanding what we mean by 'offensive.' We're not talking about a sweeper that uses trapping moves to do its job. There are obviously not enough powerful trap moves to do that. Instead, we're talking about a mon that can use the benefits of trap moves to put pressure on the opponent IN CONJUNCTION with other offense-oriented moves. Strong attacks, good coverage, pivoting possibly, etc. Implying that the only use of trap moves on an offensive mon is as an attack with an extra benefit is honestly just wrong, and not what was asked in the original question six (notice the "alongside [other moves]" part. Also, why even bring up 4MSS? Yes, it might occur with the offensive variant depending on how the rest of this goes, but defensive sets violate 4MSS
far worse. Think about it. You need 1. the trapping move, 2. the passive damage move (because a weather setting ability isn't going to do much if the opponent is carrying lefties), and 3. a probable healing move. That leaves exactly ONE SLOT for an attack of choice, in which you allege can be fitted a wide plethora of options. I'm sorry, but that remark didn't even consider your own strategy. The rest of the paragraph that follows that quote, bar the last sentence, is essentially the same as my second rebuttal, so I don't feel the need to address it any further.
On top of that, you've got potential to discuss things like Perish Song, or maybe even an Unaware+Swagger combo (although I'm lairy of that gimmick) which otherwise just flat out do not work without the trapping or binding moves moves, and simply take too long when you have a more fragile purely offensive pokemon.
So, I have to ask... you literally say here that offensive Pokémon don't run defensive sets, which is common sense, but then you allege that's a bad thing? Why should an offensive mon be running defensive sets in the first place? I cite Cawmodore as my principle example here: defensive sets on offensive mons
shouldn't be working, and if they do, then it's not really that offensive of a mon (for OU at least). You're also implying that an offensive trapper must be fast and fragile, which is not at all the case. For a pivot based mon, maybe that's a more solid argument, but offense, as I've stated before, comes in many forms.
And to wrap this part of my post up...
A defensively oriented, binding move focused mon that has multiple 3-move Sets which can be dropped and splashed around will be a much more preferential pokemon from the CAP Process perspective, and can effectively adapt to the metagame as further CAP's get added.
As I've already pointed out, binding moves are not necessarily the best choice for a defensive, passive damage/debuff/stall TrapCAP, and 4MSS affects this strategy quite hard due to the sheer amount of move types you need to account for. I don't disagree that having many sets is a good thing. I understand that quite clearly. However, with all the more niche options provided to the defensive orientation, I don't completely trust that it can truly differentiate its sets from the other main sets, and I would hate to see abilities (which have been identified as a major boon to the idea of trapping) dedicated solely to one or two specific sets. It seems far more limiting that the offensive variant.
TL;DR: Supportive-Offensive variants of TrapCAP are equally able if not more able to have a variety of sets compared to defensive sets. This can be accomplished through the use of pivoting moves, Z-moves, intelligent coverage allocation, and good ability decisions. However, the most important variant in these sets will be the use of multiple trapping moves, preferably of different types to accommodate varying strategies. The interesting options Fairy Lock can offer allow it to fall into the latter category of something worth exploring as one of these "side-sets" for TrapCAP.