I haven't seen anyone come up with a convincing explanation as to what is different. I want to read minds? There is a spell for that. I want to move something at a distance? There is a spell for that. And so on.
You are putting the cart before the horse. It's different because of
what it is and
how it does it, not which specific things necessarily. Yes, there are some spells for telepathy (various, none of which do
all the telepathy things at once), there's a high-level
telekinesis spell, etc. Psionics would do them differently, package them differently.
By your lights, there never should've been a distinction between Arcane, Divine, and Primal magic, since they all do mostly the same things anyway. But there is a difference. That's just a
thing D&D is going to have to live with from here on. Likewise, Psionics as its Own Weird Thing, whether that be "just another spell list" (that's pretty much how PF did its "occult" stuff), or basal powers that get stronger and more complicated the more points you invest, or linked "trees" of powers where you can't pick a new tree very often, or...etc. Some one of these things will need to be picked--by WotC, because the community will
never settle on its own--if WotC wants to actually make psionics work in 5e.
2nd edition is Johnny-come-lately to me, and the last edition to have a psionics class ended 11 years ago. That's before 2/3 of my group played D&D. And there was never any psionics in Original or Basic D&D.
So what? You're being entirely unserious when you dismiss
nearly 30 years of D&D history as "just three editions". Who gives a wererat's arse whether 2nd edition was your starting point? Why does it matter whether most of your players started with 5e or not? Neither of those is even remotely relevant to the question at hand, and it's not in any way a meaningful rebuttal to the factual claim that,
other than 5e, every edition of D&D proper has had at least one distinct psionic class.
Like, are you for real dismissing
literally the entire history of D&D since the moment you joined it? Do you not see how ridiculously biased and warped such a standard is? "Well it wasn't done that way when I started, therefore it has no reason to exist" is not an argument anyone on this forum would accept, and they'd be entirely right to do so.