then you're essentially changing the high tiers. no sheik main will stand idly by in a bad matchup. they will switch. in fact, many would say they must learn zelda. the sheik/zelda character will no longer be just sheik, and that's a big change for those maining her.
downB won't be the worst move in the game anymore. it'll be hugely buffed.
edit: for the sake of clarity, let me give this a scenario.
okay, let's assume these things are true: sheik/puff matchup is bad, zelda/puff matchup is good. sheik/CF matchup is good (heh), zelda/CF matchup is bad.
so, you meet up in brackets vs a puff/CF player. what does he do? can he even counterpick this player? according to characters, he can't. can he counterpick stages? at a much lesser degree, yes.
player stays one or the other of S/Z for first stock. switches to other character. no matter how the opponent plays this, he'll be at a disadvantage. this is my problem. no sheik main would not consider this. neither would a zelda main, how few they are.