Personally I’m more irritated that the franchise was for a time following the rest of geek culture and going the “multiverse” route.
I'm inclined to agree with this - mainly because trying to use the multiverse theory as a free pass to not have to try to keep the series consistent and turn any failure to keep consistency into a "clever Easter-egg hint towards multiverse theory" or whatnot pretty cheap. Yes, RPGs with inter-player interactions in general have a few inevitable inconsistencies (it can't be definitively decided exactly
who stopped the evil teams or captured mewtwo for instance - several players did so in their own respective game), but making it that, for instance, one player has to claim their gen 6 game and gen 7 game aren't in one collective universe, as there are clearly inconsistencies between the portrayals of the characters that appear in both isn't something that has to be done, and I'd personally prefer if the games were all made with each other in mind rather than using multiverse as a free pass for the creators to ret-con as they please and try to make like they're somehow enriching the canon that way. If you ask me, retroactive continuity is an easy way out, and trying to polish it up as an indication of a multiverse doesn't change that fact.
As for questions regarding what the "canon" iteration of the player character entails, that does seem a bit silly to try to argue - certainly regarding the games themselves. While some of these characters might have portrayals in non-game media (i. e. in the Adventures manga, Red's canon starter was a poliwag, and in the anime series, May's canon starter was a torchic), it does seem reasonable to treat separate media as having somewhat separate canons, while treating the games as not having anything which is left to the choice of the player as having a canon choice.