Let me respond by saying that "neutral" is not the same thing as "platform/flat stage." Furthermore, "I like/don't like those stages" is not a valid reason for (not) including a stage in the random/counterpick set.
The Klaptrap is, to the best of anyone's knowledge, random, with constraints on the max/min time he can appear again. The falling blocks on Green Greens are, to the best of anyone's knowledge, random. These random elements can cost a stock at 0% or save a person from sure death. That's not the end of the problems with these stages though. Japes is imbalanced towards characters who can't approach well aerially, and Green Greens is imbalanced in that it is small, lasers can go JUST above the center platform from the side platforms, and recovery imbalances when under blocks. Any of these things BY THEMSELVES for the stages is not ban-worthy in my opinion, but the combination is just too much. To reiterate, randomness which can DIRECTLY make an immediate difference in stock, coupled with inherent imbalances leads to my opinion that they should be banned.
I'm glad people like the other stage ban idea. I think it would only be implemented in brackets, not in pools. That way you get mostly people who pay attention to rules. And seriously it's not a difficult thing to remember. And there's none of that "What are you banning?" "I dunno, what are YOU banning?" bull****e.
As for counterpicks "unduly" favoring one character or another, "unduly" is subjective. Keep in mind that the whole point of counterpicks is to give you an advantage in the matchup, and that stage bans exist. True neutrality is a mathematical impossibility anyway (unless it's a ditto with symmetric starting locations, and neglecting controller port advantage). Mute is far from an auto-win for Jiggly, though in many matchups (but not all) it is her best stage. Brinstar isn't even close. Mute and Brinstar are also good for other characters besides Jiggly. If you think fighting a Jiggly on Mute is hard as Fox, try fighting a Marth on Mute. Fox just never gets taken there because Marth has even better stages, but it is a tough fight. Against Jiggly, Fox can just up B RIGHT AT Jiggly from under the stage and it's hard to deal with; Fox also has very little lag upon landing from his up B. Poke Floats, in my experience, is no better a Fox stage than say Pokemon Stadium. If anything, Falco's double/triple shine off the top is more powerful. So, again, Mute is not an auto-win for Jiggly, Jiggly has better stages for some matchups, and Mute favors people besides Jiggly as well. Green Greens and Corneria are going under their own reviews as well.
Regarding that, again, I don't see how we can allow Corneria and NOT Peach's Castle and be consistent in our reasoning. They must either both be on or both off. To my mind (I know I'm in the minority in this opinion), Peach's Castle is a more 'acceptable' stage than Corneria.
Now, why DK64 and Rainbow Cruise on neutral? Don't forget that if this is implemented, it comes with a RANDOM RESET. First, the idea of neutral stages is to have a stage SET that is overall "neutral" (which again can never be perfect, only an approximation). This does not mean that each stage must be neutral, but that the imbalances in each stage, when added up over all the stages in the neutral set, should be averaged out. The addition of DK64 and RC AND THE RANDOM RESET accomplishes a greater overall neutrality than the neutral 6. You don't ever have to play Cruise if you don't want to. I think Cruise is a good anti-camping stage. Sure, you can just follow the leading edge of the stage, but at the risk of a quick death. And you can camp the trailing edge of the stage, but then you are forced to move at a certain rate, and the opponent can approach you on his own terms. The stage's different parts are suited to long-range styles and in-your-face styles at different times. The stage is 100% non-random, it moves in exactly the same predictable way every time.
But this brings up one other point. Neutrality or balance only makes sense in the context of a ruleset. Any change in the rules changes the balance of the game. Conceivably, a ruleset could be constructed that balances Pichu with Fox, even if it is something as contrived as 'Fox has to forfeit a stock each match." So the question really is, how far are we willing to go with our rules in order to achieve balance? Fox, Falco, Marth, and Sheik are top tier because our rules allow them to be. The first reasonable (if any) changes that can be made to the rules involve the stages. Neutral does not mean 3 platform/flat stage, it means balancing the game.
Lastly, let me just do a blatant appeal to emotion: Aren't you tired of the same rules the whole time? Don't you want to have some goddam fun with the rules for once, especially since Melee has 2 months of life left, and Melee will most likely be a side tourney the rest of your lives? And don't you think it's good to have experience with different rulesets, since different regions do things differently? In the Midwest, they have something called the Ship 10, which is the neutral 6 plus Cruise, Floats, Brinstar, and Mute, ALL ON RANDOM. Ignore the rules of other major tourneys at your own risk.