Thinking about this, I think the reason that there's never going to be a consensus on psionics is that some people want it for what it is, while others want it for how it's done.
Looking at "traditional" psionics in fiction--old pulps, X-men, whatever--there's nothing psionicists do that can't be done via spells. Telepathy, mind-reading, telekinesis, mind-control... There are spells for all of that. You could--not saying "should," but "could"--just take a whole bunch of spells from the PHB, say "These no longer require V/S/M components," and call it psionics. And you'd be able to do everything you need to do to call a character a psionicist.
And if that's how it had been done over past editions, I think people would be fine with it.
The problem is, past editions chose to come up with brand new systems for psionicists. And because they did, it's become necessary in the minds of many players. (I say that as neither support nor condemnation. I'm not saying you're right or wrong for feeling this way.)
It's basically a self-feeding cycle. Taken in a vacuum, psionics don't have to be dramatically different in terms of system/mechanics. But because they have been, people want them to continue to be.
Thus, bringing us back around to my initial point. If you want psionics purely for what they do, a largely flavor-based UA article should probably do it for you. If you want them for how they're done, it almost certainly won't--but I don't know that you're likely to get what you're looking for until a 3PP license becomes available.