I'd like psionics to be it's own subsystem. And then a couple of options. Psionic subclasses to leverage the existing framework as the primary. No one is going to say that the flavor the the fighter is so overwhelming that it can't mechanically support a psionic fighter.
I'd also like other ways a DM can introduce it. On the character side that's primarily feats (like Martial Adept and Magical Initiate do now), but also a "wild talent" check because of Dark Sun and history - but with a penalty elsewhere to getting a wild talent so it's balanced at the table with non wild-talent characters. (Unlike 4e Dark Sun, that made most wild talents just ribbon features, I was picturing wild talents as actually being meaningful so they would need an offset.)
The other half of the DM part is monster rules, including updates for the psionic monsters like illithids such that psionics doesn't feel like it's one way for players and faux magic for monsters. So a DM running a setting without psionics can use the base monsters still.