Most of your post was talking about the cp system. The system outlined is not a counterpick system. It is a system of stage selection in which the concept of counterpicking stages is so muted as to not really be significant as stage striking covers the whole set (character switching is allowed, but it invokes a new stage striking procedure to prevent people from switching characters to exploit stages). This is why I didn't address the majority of it; the majority is assuming the existence of a system that I was assuming did not exist. I'm sorry; I suppose I should have pointed out the issue there more directly.
You raise a new point in your latest post about stages being disliked. To me, that seems like a major deviation from an originalist philosophy. The constructionists ban stages because they dislike them. If a stage like Shadow Moses Island is in the mix, I see two possible outcomes. Either the match-up is one in which it is a significant advantage for one side, and in that case it will be struck by the other side (if a player can't play out currently banned stages from the winning side, this is a major weakness that I feel should rightfully cripple him). If it is a match-up in which the stage is mostly fair, why does anyone have to strike it? Maybe it's a stage that should actually be used. Isn't their personal preference clouding their judgment on the true game in this case?
I disagree with your use of some wordings in your posts. No stages "unnaturally" do anything other than perhaps custom stages. The stages are in the game. Therefore, they are natural components of Brawl. If we decide to "defy nature" to make something better, that makes sense. However, to deny that nature is nature seems bizarre to me. At best, this is saying that mosquitos unnaturally spread malaria in tropical regions. Yeah, no one likes malaria, but this process is incredibly natural.
The use of the term "competitive" also bothers me. I'll reference a definition of "compete" here, the root word for competitive:
to strive to outdo another for acknowledgment, a prize,
To me, exploiting broken stages seems perfectly competitive. Indeed, every player should be trying with any rule set to find broken tactics and exploit them mercilessly. To do anything less is the truly anti-competitive thing.
Skill is another fuzzy term. Here's another dictionary definition:
the ability, coming from one's knowledge, practice, aptitude, etc., to do something well:
The only meaningful way to interpret "playing Brawl well" is to win your games. Therefore, skill is your inherent ability to make yourself win. If you fail to strike a stage like Temple from the losing side, you are showing a lack of skill and losing in just as legitimate of a fashion as being outplayed on Battlefield. I see Temple in no way taking away from skill in a procedure as I earlier outlined (though it's obviously a problem in a counterpicking system).
You raise the point of two extreme outlier stages in this game: WarioWare and Mario Bros. I would first point out these are the only two stages that are particularly unpredictable; every other stage that is banned is perhaps very exploitable but is not inconsistent in any meaningful way. I can think of tons of shenanigans on Skyworld, but nothing is going to randomly make me lose. A loss on Skyworld happens either because the other guy had a better character for the stage (my fault for not striking it then!) or because the other guy is better than me either in general play or in ability to take advantage of Skyworld (both highly legitimate ways to lose). Anyway, as per the two stages in question, first Mario Bros. This crazy stage is in fact so crazy that I don't think anyone actually knows the long term implications of it. I like to make jokes that it's the most fair stage in the game because anyone can win at any time, but really, I don't know. There are only two real random factors on it. The first one is the spawn pattern of the monsters at the top, which is observable easily and can be reacted to. The other is the fireballs, which spawn in set locations even if at seemingly random times (I know of no study of this!). The gameplay is crazy because of the power of the hazards, but it's entirely possible that players could control this. If some player investigated Mario Bros. deeply, grew comfortable playing on it, and began refusing to strike it in tournaments, is it that unreasonable that he would be rewarded? WarioWare is more directly random, but it is still far from completely degenerate. The stage is tiny, and the games are playable. It introduces a probably unacceptable random element, but it's not like the game becomes a true 50/50. In many match-ups, I suspect the geography is more significant than the randomness and the stage gets struck that way. In other match-ups, it becomes a game of chicken to strike this one stage, and in that case it's kinda a battle of wills which is maybe overall not that bad if nothing else.
I'd really like to stress that Mario Bros. and WarioWare are the only two stages that have potentially serious issues with unpredictable results. Other banned stages are just straightforward broken in some match-ups (Temple) or maybe not deserving of a ban at all under even normal rules (take your pick).
As per characters who benefit, I'm questioning how far this really goes. Walls and walk-offs are the most exaggerated boogeymen of smash. This game has 666 match-ups. I question whether any particular wall of walk-off configuration on any stage even breaks 100 match-ups. The abuses are fairly small in number and contained well within specific characters. The main two benefactors, King Dedede and Diddy Kong, are arguably pretty fair ones here. King Dedede has a growing consensus of "he's not that great" maybe being able to push stage selection like this is an important thing to keep him competitive. Diddy Kong is hurt by a lot of the other stages, and being able to rely on the opponent striking walls and walk-offs seems like a very fair balance (he'll be striking all the heavy aerial stages in the meantime). I'd really stress that most characters see different benefits different ways. It's mostly a different set of characters that like Eldin versus Flat Zone 2 versus Shadow Moses Island.
Loops are pretty limited. In terms of real "hard run-away" stages, you have Temple and Spear Pillar as nearly pure grounded loops and Hanenbow as a nearly pure aerial loop. New Pork City is a hybrid loop between aerial and grounded, and Summit is a loop with unusual physics. There are some arguments that 75m, Rumble Falls, and Big Blue are runnable, but there are going to be a pretty large number of match-ups in which neither side can run them. Mario Bros. is maybe workable as a loop, but that stage is too crazy for us to really judge accurately. Sure this sucks for Ganon and Bowser, but I'm not sure the majority of the cast is really too bothered by the striking implications of these guys.
Then you have a stage like Skyworld that is just banned now for being a really, really powerful counterpick. In a system without counterpicking, how do you justify banning that one?
I'll cut ahead to a few of my fuzzy predictions of what the actual balance implications would be...
-Meta Knight stays the best but probably doesn't get better. His aptitude at running loops mostly just saves him from how bad he is on a lot of other banned stages, making it a wash for him.
-Snake and Falco fall but remain good. They maybe drop from top to high.
-Diddy Kong maybe falls a little but not much. King Dedede remains nearly in-place.
-G&W, Pikachu, and Wario all rise a lot. They are the three most likely major benefactors.
-Ice Climbers end up a lot worse but still overall competitive. They maybe go as low as mid tier.
-Most other decent to good characters (Marth, Pit, R.O.B.) don't really move much. I admit that I can't predict Olimar in particular.
-Jigglypuff moves up a lot among low tiers but remains low tier.
-Ganon somehow gets a lot worse, much to the amusement of everyone. Bowser kinda goes down along with him but maybe not quite as bad.
If you have different conclusions, feel free to let me know. I don't want to turn this into too much of a derail, but without using logic that ultimately leads to constructionism, I'm finding it hard to stay away from this business.