this is kind of silly though, because while all cp-stage talk seems to revolve around the fox vs peach matchup for whatever reason, some characters just suck on both (marth, ice climbers, etc)
it's not like just because peach has an advantaged stage, fox deserves one too or vice versa
Honestly, as I said before I think the most neutral setup would be what SPOCVIII had (7 neutrals, stage striking) but personally I enjoy having more stages, as do a lot of players.
Just going off memory, the standard ruleset is (correct me if I'm wrong)
Neutrals:
Final destination
Fountain of Dreams
Dreamland
Pokemon Stadium
Yoshi's
Battlefield
CPs:
Corneria
Rainbow Cruise
Japes
Green Greens
Brinstar
Mute City
Pokefloats
Kongo 64
Of these, for the majority of matchups, Fox/Falco lose stages like Corneria, Japes, Green Greens, and Pokefloats, plus Stadium is a CP now. Jiggs/Peach lose Mute City, which was basically an auto win. I don't ever use Sheik so I don't know how she does, but Marth's don't often CP those stages, they usually CP neutrals, and avoid going to most CPs/Dreamland when possible. CFs usually go to FD, Dreamland, Yoshi's, or Kongo, all of which are staying. (I think I covered all the high/top tiers...)
Not gonna go into lower tiers, because I don't know much about them and there are a ton to worry about, but the spacies and Peach/Jiggs seem to have lost the most of the "tourney viable" characters, which is why they're the ones whose CPs are under discussion. Plus the stage striking is pretty nice for Marth and Sheik as is, lol.
Not saying my opinion on whether or not they should be "linked," just saying why I think they could be seen as that way.
Edit:
Question: why are there counterpicks? usually the counterpick stages favor some characters greatly and it turns out that the winner on the counterpick wins less on skill and more by stage advantage/luck. probably a stupid question but can someone just answer it really quickly?
Theoretically, if the first stage is perfectly neutral, the better player will win (isn't always true, but yeah).
Then if the second player counterpicks a stage, they will (again, theoretically) still need to be close enough in skill to win against their opponent on that stage. If they do win, it could give them the momentum they need to win the next match (at a stage disadvantage).
It should only make a difference in matches where players are very close in skill. But that relies on the fact that neutrals are neutral (or will come out to be neutral, through random or stage striking, over time/a large number of matches) and counterpicks are never an auto-win/players still have to be close to their opponent in skill to win on CPs.