YES, YES, AND MORE YES. I'VE BEEN DYING TO SEE THIS MADE.
(A lot of what I have to say on this subject are from YouTuber joshscorcher's "Pokemon Done Right" rant. If you want examples of what I'm talking about, see that.)
When Nintendo finally does release a console that has the power to support an MMO for Pokemon, here's how it should work:
You are given the choice of going to ANY of the regions: Kanto, Johto, Hoenn, Sinnoh, Unova/Isshu, maybe even Orre. (The storyline with the evil teams will probably have to connect somehow in order for this to work.) When you start off, you choose a name, a class that will give you a bonus, a hobby or secondary class, etc. You play the game like you would in all the other ones, beating NPC gym leaders and the Elite Four. Once you beat your region's league, you can travel through the other regions, as well as enter a special league that uses real people as Leaders and Elite Four Members. Interaction with other players can happen anywhere and anytime unless it interferes with the storyline.
I'll put up other ideas as they come.