It would be shit. People complained about how Bayo 2 wasn't on the consoles Bayo 1 was already on, and that happens every time a sequel comes out on a different console that the original or it's successor.

Outside of the karmabait, your request is "Give me a series that is inconsistent in every way and spread across 3 different exclusive platforms with different controls". It's an absolutely terrible idea just for the fact that it requires you own a PS4, Xbone, AND Switch just to play it. I know this is /r/gaming and some people here own all 3, but most gamers aren't extreme enough to buy all 3 of those, it just limits the series in a terrible way where the 1st in the trilogy might be fine, but the 2nd and 3rd games will sell like shit because of how few people could play them.

All you would get is a series where every game is nothing like the other ones, and not in a good way because even the characters would act completely different because different teams made them, and the themes and stories sure as hell won't line up well. The three companies are not similar at all, there is a 0% chance Nintendo would make something that would line up with Sony, let alone Microsoft.