This entire argument is based on assumptions and fallacies:
1) "When competing in a tournament it’s obvious that contestants should only rely on their own abilities in order to win."
Obvious to who? Why is it obvious? There are plenty of people who think coaching is perfectly fine. It's not obvious at all that players should have to rely only on themselves.
2) "I don’t think there is any person who thinks it should be legal to pass your controller to a friend and have him win a match for you. Well, I’m here to argue that coaching is the mental equivalent of handing your controller to someone else."
This is false equivalency. Getting tips from a coach =/= mentally handing over the controller. The mental decisions which truly influence the outcome of the match are made in real time during the gameplay, and those decisions are still made solely by the player. Good coaching helps the player to make the right decision in those moments.
3) "To understand why that is we must first answer a simple question. What makes a good player?"
This is begging the question. The OP is not actually asking what makes a good player, but is instead presenting a circular argument about skill to prove the assumption he's beginning with: coaching is bad.
4) "When you coach someone during a game, you’re helping them adapt. If people did this during chess it would be obvious why it’s a problem. Chess is a game of decision making. It’s a mental contest, so if someone’s helping you with decisions, they are playing for you.
Though execution is clearly an important factor in Smash, decision making is also a crucial part of the game. So if someone is helping you in that aspect, they are playing for you. It's essentially 2 vs 1 at that point."
See #2 above. Also applicable to the steroid comparison.
5) "For it to be fair, every player would have to register with their coach before the start of the tournament. Coaches cannot enter singles. One coach per player and vice versa. This is impractical if not outright impossible given the structure of our community."
This is an ambiguity fallacy. Why should coaches have to register? What would that accomplish exactly? Why shouldn't coaches be allowed to play in the tournament? The OP has said this needs to happen, but doesn't say why it needs to at all.
5) "Even if coaching could’ve been done in a fair and balanced way, it would still be a move away from the skillset that we as a community value and want to test -- execution, adaptability, and mental fortitude. Devaluing adaptability is a step backwards."
How does coaching devalue adaptability? The coach may point something out, but in the end the player either makes the adjustment or doesn't in actual gameplay. There are still dozens of tiny adjustments being made in-mat1ch that coaching can't account for. Adaptability is exactly the same whether there's coaching or not.
Coaching should allowed because there really are no compelling arguments against it. These discussions almost always boil down to the fact that people opposed to it don't like it, but that's not a sufficient reason to ban the practice. As for the people who say that it takes too long and drags out the tournament, is it really that much worse than the hand warmers and button checks which players do as well?
1) In some professional sports such as tennis which is in fact very similar to 1v1 Smash in an analytical sense, coaching is not allowed under any circumstances while on court which includes washroom breaks. It is entirely up to whoever is playing to determine which changes/adjustments need to be made. It is much easier to see these habits and areas of improvement, etc. if you are not the one under pressure playing.
2) I agree to some extent, but the point is that the competitiveness/mindset should come from yourself as opposed to using a coach as your "crutch". Your response contradicts when you discuss coaching not having as big of an impact. You need to choose a stance versus swinging based on convenience.
3) I don't think you understand what a circular argument is... It makes sense that his arguments support his point of view (kind of the purpose of making arguments) and he gets extra credit for anticipating some responses and answering accordingly.
4) I do not like saying this, because I prefer to break down the argument before rebutting it, but this is just plain wrong. As I pointed out, you are contradicting yourself for starters, but in games such as chess or Smash, letting someone else choose your gameplan during a match is essentially like having a partner. One of the things that makes "smart" players so successful is just that versus their tech skill. Players such as M2K are examples of this as they do not have the best tech skill (M2K has really good tech skill, but I would say that there are a number of other players who are better at it) and are not making these ridiculous combo videos, but have such a good grasp of the game that they just know how to win. You are essentially cutting out a large part of that part of the equation if you allow coaching.
5) This should be obvious in that if a coach is playing, they cannot coach a player at the same time (cannot be at two places at once) - if one player has a coach while the other does not for this reason or that they are coaching another player, it is unfair. By locking pairs together, it ensures that the coach will always be available for that player and that all players who want a coach will have one.
5) Adaptability is based on knowledge/understanding and as I mentioned in #4, many players are great because they have that ability to combine decent tech skill with the experience/knowledge to adapt - so yes, coaching devalues a player's ability to adapt.