I very strongly disliked psionics as they existed in AD&D for a few reasons:
1. They were implemented as an extremely powerful bonus for the occasional lucky player, making their character instantly far more powerful than others.
2. They felt out of genre, like 70s soft sci-fi getting stuck into fantasy. That just wasn't to my taste.
3. IRL, the notion of psychic powers generally irks me because there are too many people who insist that they are real, and I didn't like all that pseudo-science getting stuck into my pastime. Few people insist that magic is real, but call it telekinesis or whatever and suddenly a surprising number of folks take it seriously.
They don't bug me as much in other settings - like a science fiction one.
In terms of game design, I don't really love having a whole other system for something that is just another flavour of magic. That said, if it is limited to one class, like ki points, then it's not as big a deal.
Overall, I do not prefer psionics muddying up the core rules, but could see them as a setting specific thing, like for Dark Sun.
Addressing the OP: for practical purposes, they just seem like magic from a different source, which the current rules handle just fine (c.f. clerics, wizards, sorcerers, etc.) so I'm not sure why they would require a new system. We already have plenty of "psychic" spells in the game.