They'd have to do something really innovative because if the best a bunch of fans can do is competently emulate what has already been established then Nintendo could just do that themselves. And if some fans get to the point where they can create a great fan game then they should just make their own unique IP and rake in some cash. Sonic Mania is a different story though because it's not hard to upstage the Sonic Team since they can barely achieve mediocrity at this point. The people in-charge there are either over-the-hill or so bored with Sonic that they're just going through the motions.
So you're saying Nintendo shouldn't get fans to make new games, but Sonic Team should? Or should Sonic Team just work on something way different?
I don't think Nintendo would allow fan games to begin with, especially not with their prized IPs. At most, they'll just look at the attention certain fan games get as a cue to make that game themselves.
As for Sega, they're already letting fans make games for them. Sonic Mania was a success for them so they should continue letting that team make 2D Sonic games for them. As for Sonic Team themselves, they should take a break and do something else because it looks like they're just going through the motions.