Whose to say Pauline would stop a Splatoon idol or Rhythm Heaven character from getting in too though? (I was going to add Barbara again but she really is a pretty out there longshot.)
While they all have some ties to music, I'd imagine they'd still all be handled pretty differently. I personally don't see Pauline as a solely music/rhythm based character to be perfectly honest.
You're right of course, although I guess I like to think of batches of newcomers that are each thematically diverse. Obviously Pauline and say, KK Slider don't have much business playing like one another. But both of them service the "performer" role, and music is going to be a central throughline through their character. Whether or not it manifests into distinctly music based attacks is one thing - I think KK would be more likely to actually be playing music while Pauline would use it as a general aesthetic - but I'm just hesitant to believe we would see them explore this premise in multiple ways within the same game.
That is to say if any of these characters had been added in the past - say Chorus Kids made it into Smash 4 after all. Then obviously any of these guys are still on the table to be added now. It's moreso the close proximity of characters who are both thematically comparable and stem from a character premise that has yet to be explored at all. If we've gone 25 years and the closest thing we have to a musician character is Jigglypuff, then I'd say the likelihood of getting two of them at once feels pretty slim. Although admittedly I'm also trying to temper my own expectations, as a musical character in general is maybe the character archetype I'd like to see the most next time around, and IMO one of the most unfortunately absent from the roster as a whole.
I'm also inclined to say Pauline would cannibalize the odds of a Splatoon idol / duo specifically. Both would likely involve emphasis on dance moves / choreography, and use music as a backdrop but not necessarily the exclusive focus. It's easier to say someone like Chorus Kids could exist alongside Pauline, because I think their potential is just its own abstract thing altogether. But the showy performer type character has a pretty stark overlap here, and between say Marina and/or Pearl and Pauline I really think Splatoon should get the nod. It's a far more important part of that series, anyway.
It feels like the hype for Pauline to join Smash is primarily just there because Odyssey both brought her back and made her more popular.
Also not to disparage those who actually want Pauline, but I feel like you're misconstruing hype with general conversation here. Pauline is not an intensely popular request for Smash, she's just been popping up more frequently. So her recent prominence makes her someone worth keeping in mind, and talking about and maybe trying to see what can be done there. That seems to be where most of this comes from, less so any passionate movement in her favor.
Again, I'm not saying people don't want the character. I'm just saying she doesn't keep coming up because there's "hype" behind her, it's because she keeps showing up in Mario games and people are getting Rosalina flashbacks.
I'm still hoping that we get a Rhythm Heaven character.