As someone who has never played with psionics in D&D, can you expand on why you believe psionics would require a different combat system?
2e Psionic Combat and Psionic Powers were two separate systems, though Psionic Powers sometimes interacted with, or triggered, Psionic Combat.
Psionic Powers essentially functioned like Spells except that they had Power Point costs and different aspects of the power that you could change by investing more points into it. This is back when D&D Spells didn't have a "When cast from a higher level slot" option but spells instead scaled with your level (A 6th level Wizard's
Fireball did 6d6 while a 10th level Wizard's
Fireball did 10d6, both for a 3rd level slot)
Psionic Combat was a whole different beast basically meant to mimic going into someone else's mind and fighting them there. Something like this:
Or this:
In reality you stood there, while brain-battling. It was pretty cool in -concept-, obviously. But in play? It meant the entire table ground to a halt as the Psionicist player spent 20 minutes rolling various attacks and defenses against the DM while other people twiddled their thumbs.
It also applied to stuff like two Psionicists trying to use Psychokinesis on the same object. They'd do roll-offs to see who could control it, sort of like brain-wrestling instead of arm-wrestling.
And, to be clear: I don't "Believe D&D needs" that. In fact I think it's better left as a relic of the past. As cool and thematic as it is, it doesn't translate well into game terms or playscape sharing. Which is the reason that I mentioned never seeing a designer try and model it into 5e D&D.
I've never heard of anyone who tried to have sex with an in-use Blender. Acknowledging that doesn't mean I think people -should-. Just means they haven't to my knowledge.