Would be kind of neat if Pokemon HOME is kind of like Pokemon Ranch and you can watch all your Pokemon do all sorts of stuff.

Maybe throw in some Pokemon Stadium-esque minigames, too?

OR JUST MAKE IT SO THERE'S A BATTLE MODE LIKE STADIUM. You import your Pokemon and can pick them to use just like in Stadium! And it's online already!

Keep the adventuring/catching/filler to the Main Games, and have HOME be a Super Storage/Battle Hub!