I don't think it's possible to make a psionics system that is distinguishable from the existing magic systems, isn't overpowered, feels like it would fit a fantasy game (instead of relying on all the modern and SF terminology like it always has in D&D), and can be run in a way that isn't clunky and will be liked by a majority of the players.
I think this is kind of silly point, not intending that as an insult, but just seems a bit thoughtless, because the same really applies to magic in D&D.
If you had D&D with some other magic system, and you tried to introduce D&D's current magic system, people would loathe it. The reaction to any psionics system would be highly positive by comparison. The idea that the "majority" of players "like" (rather than tolerate) Vancian casting seems to me to be an incredibly questionable one. So to me you're demanding a complete double-standard. I think it would be absolutely possible to add Psionics that were distinguishable from Vancian casting (just use power points, it's not hard), not clunky (again, assuming current magic isn't "clunky"), and tolerated by a majority of players.
That's the big problem that WotC themselves didn't understand. Vancian casting as implemented in 5E wouldn't pass their own standards (what was it, 70% approval?). The casters in 5E wouldn't pass their own standards, they wouldn't even come near - full casters would be immediately dismissed as ludicrously overpowered, a joke even. Each class would be lucky to reach 50% approval if they were actually being presented as new classes.
But if you lower the bar to the same actual level, the real place the bar should be, you're looking at tolerate. If they'd done that, the Mystic with some balance fixes (far smaller than people like to suggest) would have been fine, and distinct enough.
Anyway my one thing would be a power-point based Psionics system.
Where in D&D has it been done "right," though? Every incarnation of psionics I've seen for D&D has been a mess and IMO failed in one or more of the ways I listed.
So has magic in every edition of D&D (except 4E, which non-coincidentally, also had fine Psionics but people like to say it "wasn't D&D"). This is just a double-standard and nothing more.
Personally, I like the psionic archetypes and wouldn't mind more of those, but I honestly can't stand the idea of a psionic class.
I think this is the real issue - you don't like the idea, fundamentally, and the logic and double-standards you're applying are just backfilling on a decision you've already made, rather than actual arguments.