So instead of one system that's not great, you'd have one system that's not great plus a system that is one or more of (A) just like the first one, but we'll pretend it's different, (B) overly complicated, and (C) either underpowered or overpowered. I can forgive the foibles of the magic system (especially since I find it much improved in 5e), but both magic and psionics is a bit much for me.
This isn't a rational or reasonable approach, sorry mate. There's no actual reason it necessarily has to be those things.
And that's not even getting into game questions of how psionics and magic affect one another or what powers brings to the table that magic doesn't, or shouldn't (do we go so far as to edit the spell lists so there are things that only psionicists can do, in the same way there are spells only wizards can cast?). Or worldbuilding questions of why and how both things exist in the same world.
These are utter trivialities, especially in 5E. Not real concerns at all.
That being said, you still haven't said which incarnation of psionics was done "right." I honestly do want to know what you consider to be a good D&D psionics system.
I liked the 2E, 3.5E, and 4E systems.
2E worked weirdly well, it was breakable, but it was the 1990s, let's not pretend everything wasn't breakable, but it was a fun system that a lot of players seemed to like, at least who I played with it. It certainly didn't seem over or under powered, particularly.
3.5E is a bit Marvel/comic-book for my liking, but it was quite fun and worked pretty well. Better than most things in 3.XE did anyway.
4E's psionics stuff was just beautiful. Obviously hard to translate to other editions in terms of mechanics, but the fluff and classes was really cool.
5E's Mystic was absolutely fine and the only thing wrong with it was it needed about 1-2 more rounds of balancing. It would have been perfectly good. WotC got obsessed with their own dumb metric which would have stopped them ever adding a full caster, and applied a double-standard, and we didn't get it. I feel pretty sure if the Mystic came out today, they wouldn't apply the same foolish metric in the same mindless way, because it's a very different WotC now.