Yes
@Kobold Avenger, I would like to read your reasoning. My copy of 2e Complete Psionics Handbook, was destroyed many years ago, (along w/ most of my 2e books), but from memory, it was to my mind
the best stand alone Psionic system to date.
Psionics should not be completely foreign from the existing rules especially if it was introduced in a book outside the core books. 2e's was the worst because it was so different, and had 2e had about 2.5 different versions of psionics with the Complete Psionics Handbook and the horrible psychic contact/tangeant rules (best defense against Psionics, is don't be psionic), and then Dark Sun revised which threw that system into the garbage, and then Skills & Powers.
For the first iteration, many powers didn't work at all if the psionicist didn't have psionic contact, which they had to do through the convoluted psionic combat system which they needed about 2 wins to get 2 tangeants. Meanwhile most of the other powers unless they were Disentigrate or Detnotation were quite weak. The Psionicist despite being conceived as being close to a Wizard, had nothing to stand up to it. And that was before they dumped that system once the Revised Dark Sun campaign setting came out in favour of things like MTHAC0 and Mental AC.
Once the D20 system was solidified in 3e, it showed that having powers based on skill rolls wouldn't work, as the non-psionic Truenamer which using skill rolls proved. Skill rolls to use powers either gets too difficult as levels go up such as the Truenamer had, or they just become so simple they are irrelevant that one shouldn't have bothered with them in the first place.
3.5e psionics had levels which was familiar enough to balance with equivalent spells, it introduced enhancing powers, that every spell-casting class in 5e uses now. It certainly had it's problems like making the "nova" too common, and new spells that should have been on the psion power list still had to be rewritten for psionics, if they remembered to do such a thing.
The major thing about having a different system, as explained before a bunch of times, is that even though the player might like it, the DM doesn't want to learn a new system just to accommodate one player. It would go something like this:
Player: I want to play a psionicist!
DM: That class is completely overpowered, they can get disintegrate at 1st level and override magic and so on....
Player: But it's different now, it's balanced and everything, see this...
DM: I don't have time for this, f#@! off!
If they stick to using spells, I think that same scenario will turn out differently. As it'll just involve getting used to some new spells.