I've never played a Rhythm Heaven game, but I think I've figured out why Sakurai might have picked them over the seemingly more obvious choices like Karate Joe or the Wrestler. Those two are fighters, so they've got obvious moveset potential, but this is, ironically enough, exactly their problem. Rhythm Heaven is in no way about fighting, it's about music, so of course you'd want to represent that through characters who are inherently musical.
Furthermore, they have a distinct, yet still humanoid design. The Wrestler or Karate Joe could come off as somewhat generic, but the Chorus Men, though simplistic in design, don't really look like anything but themselves. Although, the small amount of research that I've done shows me that their basic design is from an earlier RH game, and that it, apparently, is recurrent. I think this really just makes them better as representatives though, since they only look like something else that's part of the RH series to begin with.