I just want to point out a few things...
Banning is not a last resort. If overpowered items and forcing the players to play every stage in the game to determine a set made the characters all equal, you would still not do that. There are always things to tweak, like the damage ratio discussion, but no one thinks that will catch on, because it changes studied gameplay so much. Banning wouldn't do that, except to those whose lives consist of playing MK or playing against him, which is entirely sad.
Also, comparing communities is entirely flawed. What one entity does over another is no way to prove what is right. It's very obvious if one character does lord over all characters but a few even matchups, that hurts the beauty and variety of the game as it is. If you want to make MK vs MK/Snake etc it's own tourny structure, then that's fine. Having specialized tournaments is fun. But normal, official tournaments should be very concerned with clear imbalance.
When it comes down to it, if you're really only concerned with skill, you would limit everything to one character and duke it out, but that's no fun. This isn't the best argument, but there's always a variety of things in a sport-like environment... well those that don't are pretty dull and not televised sans golf and the Olympics. Interesting sports involve a variety of factors to adapt to.
So do you love the game, or the show of skill alone? There are other things you can show that in. But to me, having more variety forces more adaptation, thus more skill and fun both.
As for being more on topic: The current system is better than the suggested. Yes, coin tosses are bad. Most everyone would cry foul when they lose the toss and the game. And yes, the advantage shouldn't be too big. Providing that the winner doesn't get to strike another stage, it should be fine. And yes, the winner should be able to repick their character, preferably after the stage is chosen, possibly both players blindly. I don't think blind is necessary though since the loser can choose whether to mirror match or counter, even if the winner picks the best character for the stage. The loser has to keep that in mind when picking a stage.
I'd think the reason for CP is that it assumes there may be imbalances in the first matchup + stage, though "neutral," and allows the loser to claim they can do better with a more fair stage. (This means the 2nd match is obviously going for imba, tho can be deflected by char choice.) Along this line of thought I would never involve stages not "neutral" unless the char's were chosen first, which narrows down the maps that may be chosen to prevent a very biased matchup.
So here's my suggestion for a change, if any:
[1st match and prep for 2nd]
-Stages struck. Play on stage randomly picked or agreed on.
-X Wins, Y Loses.
-X picks character, Y picks character (in assumed claim that the matchup was somehow biased.)
-Maps are whittled down officially by stats for that matchup and/or the exploits that might break balance (or just disallow them if easy enough, like N64 Corneria's big lasers).
-Player Y chooses a stage more based on preference than balance, to get him back in his game (mental aspect).
[2nd match and prep for 3rd]
-X wins? okay, wasn't a big disadvantage. Y wins? then move on below.
-Repeating the above process (but X/Y switched) does not automatically favor X really, but allows him to not have that perceived imbalance. So do the same as above.
