I actually think D&D makes as much if not more sense as a sci-fantasy game than a pure fantasy game. (Who built the dungeons? An ancient, technologically advanced race? Aliens? The game goes in this direction easily.)
I suppose that could be taken as evidence that D&D is a miserable failure at modeling the fantasy genre...
I mean, it cribbed it's magic system from The Dying Earth, which is a science-fiction series by Jack Vance (thus 'Vancian'), set on a distant-future Earth.
This is pedantic. Psionics is in the AD&D PHB. No, not as a class technically, but it's in there (any character has a chance of acquiring psionic powers).
No more so than the "every class in a PH
1" rubric is in the first place. Only 3e and 4e have PH2's.
But, yes, psionics have long been a feature of D&D - in a supplement or appendix. But the Psionisist didn't appear until 2e, in a supplement, and none of the later psionic classes make the "in a PH1" cut, either.
I think you could make a strongish case for a 'Wild Talent' option of some sort, though. It doesn't sound like the Specialty successor to Themes is quite appropriate for that, and Background would also be pushing it, but there might be some way of pulling it off...
As for psionics not being a strong enough fantasy trope, are you applying the same test to say, Monks? Or Beholders?
Yes. Monks, while not as off-base as psionics, are too loaded with pseudo-cultural baggage, and belong in some sub-genre or setting supplement, not in the PH1 (but, they /were/ PH1, so they're in, nothing much to be done about that). Monsters I'm not too concerned about. It's much less controversial to just not use a monster (few campaigns are going to use /every/ published monster!) than to ban a class (which can leave a player bent out of shape).