I have a question: Don't Rhythm Heaven fans want a rep because the whole rhythm thing would be unique? If so, I see a potential problem with that. It would be difficult to have a rhythmic timing to button presses when all the songs in the game have different rhythmic timing. I could easily see songs throwing off a person's play if they're too different to how you'd have to time your attacks (and I'd like to note that "Environmental Noises" is a track in the game). And of course, it would probably be more of a workload than it's worth to try and make it so the character's button presses time differently with every song in the game (to which players would then have to learn the timings for tons of different songs).
And now that I think about it, perhaps this is why Sakurai ended up scrapping the character in 4. I'd bet, however, that there could be ways to work things out. People who know more about RH than me: what could be done about this issue?
I don't really want rhythm based moveset based on the music that play because that 100% unrealistic. Not only there's way too much music in the game to make that work, but the character would be impossible to balance (imagine a character being low tier when environmental noises play, but God tier when Megalovania play).
I have two ideas for the character. Either you make some moves (like the special only) timing based (kind of like Incineroar side B). I think it would still be a pretty good representation of the gameplay of those games.
My other idea was that the conductor of the Chorus kids is on the background (think of it like Pokémon trainer) and he's doing a beat with his baton and if you attack at the same tempo as the conductor beat you got some bonus knockback. This would be more close to a rhythm based moveset than my first idea, and way simpler to add than a rhythm based on the music that play, but it still create some problem, like what if there's 8 chorus kids? And maybe waiting for the conductor tempo to attack would just be awkward.
In the end, personally I don't really care that much about rhythm based moveset. Sure if Sakurai have some good ideas I would take it, but I think that with their unqiue design and unique mini games, a Rhythm heaven characters would feel unique even with no Rhythm mechanics. Also to play devil's adcocate I don't think that a Rhythm character would 100% need rhythm mechanics, as many characters from different genres in their games don't bring mechanics from their genres. For example, Snake don't have stealth mechanics despite Metal gear being the king of his genre, and JRPG characters (the Pokémon, both earthbound characters, Cloud, Joker, Shulk) didn't really bring RPG mechanics before Hero way later.
Also I don't think Sakurai cut them because they where hard to work with, but more because they where "low priority newcomer". In an interview with Nintendo dream he said: "This time our project-proposal is dated May 2012, at that time all characters were decided already. Then as production moves on we will say “We won’t put that character in” and cut out low-priority-characters." Then the interviewer ask "That means in your project-proposal there are more characters than ended up in the game?" and Sakurai answers: "Yes, but I won’t tell which of course." Source of this interview:
https://nintendoeverything.com/one-newcomer-was-almost-cut-from-smash-bros-wii-u3ds/
To me it seems that the character in question is Rhythm heaven, considering that the Gematsu leak was probably a very early draft of the game, probably that May 2012 plan that Sakurai is talking about. And honestly it's not really surprising that Sakurai would consider a Rhythm heaven character low priority considering that it's a really small franchises from Nintendo.