Real talk? I half speculate that the Splatoon team themselves may have pitched the third game to Nintendo in hopes of finally righting some of the wrongs in 1 & 2 after seeing fan feedback. Things like better netcode and save structures probably just weren't things they could achieve with patches in 2: Some of that stuff probably would have taken outright engine rewrites, so it wouldn't surprise me if they just said "Forget it" and made a whole new game so they wouldn't have to be paranoid about breaking things in the already established, large playerbase title.
Also, yeah, the new servers are apparently good. Mario Party uses them and apparently the experience is pretty decent apart from a few disconnects, but it seems like they're slowly ironing it out with time. I think Nintendo knows they can't not care forever: They're making progress, just really slow progress, lol.