I was trying to call out Sakurai's logic more than yours
That's kind of a weird quirk considering more than one character can be on a stage at the same time
I don't exactly consider it weird, this is kinda common place in fighting games. For example: UMvC3 has Tron Bonne as a background character in a stage, but that is disabled when she's selected by a player. Multiple players using the same character is pretty much a different situation, as it's something of a Gameplay/Story segregation kind of thing (or that's how TV Tropes calls it). In the end, they're still very much the same role (being a fighter) when pitted by multiple players.
I think characters that are background characters can work as a fighter, provided they don't have a real purpose to the level they cameo in (such as Dedede in DL64 and Link in Spirit Train). But characters that works as hazards won't likely make it as a fighter as long as that role exists (such as Ridley). They typically don't have anyone to be replaced with without alternating the gameplay in any way. (Conductor Link is not a hazard and does not affect the match in any way, so that was why he was able to be replaced by that other character).
The same applies to ATs. I'm unsure if Final Smash truly affects the same, but I guess that is up to debate. Personally, I think it's the same case. (Although I really don't think Chrom nor Shulk's gang has any chance for other reasons)
There's some exceptions though, like DK in 75m and Duck Hunt Dog, but these levels gives you an impression that you're inside an arcade machine or video game, so the two characters there aren't the real characters. And that impression is very clear. So that is averted.
But yeah, I think this is just how some game designers operates. So may not like it but I think it's not unreasonable to have that kind of logic.