The main thing seemingly turning people off of Rauru is simply that he isn't as popular a character as some of the others. But I don't think that's the factor to put the most weight on for this particular situation...I feel like among the main goals in choosing a BotW/TotK character are promoting and representing what those games are all about, and choosing someone who, ideally, reflects those goals both in the moveset and in their plot role, i.e. someone sort of, for lack of better description, is most "emblematic" of the source material.
While I don't inherently have a problem with choosing favorites among the Champions if there's a good reasoning for favoring one, be that from popularity or otherwise, the Champions being kind of lumped together as a group does hurt them in that regard. And, on that same point, by design they're more or less confined to one specific element or combat niche, which on its own again isn't a problem, but makes them less of a fit from the angle of the character being there specifically to rep the Wild era, more or less all on their own. If there wasn't a more clear option, I'd probably be more willing to ignore it and just go with the fan favorite here, but Rauru is a much more "centralizing" character in the sense that he stands on his own, is thematically less specialized, and is prominent all throughout the story (including, importantly, the beginning parts that all players are guaranteed to see).
Someone like Kohga also feels very unlikely to be the choice. Despite the moveset potential and not being attached to a group of relatively equal peers, he's far too much in the periphery for me to get on board with him. It's way too easy to dump a ton of hours into BotW/TotK and barely encounter him. More major villains have had a tough enough time getting represented in Smash, let alone one as tangential to the main plot as Kohga. The only remotely comparable case we have to Kohga in terms of minor/side villains getting in is, like, Wolf and Dark Pit, and those are of course are only there because they could be clones. Why would Kohga of all characters be the one to break the trend of less-recurring and non-Triforce Zelda characters not making it?