To reiterate Arkhandus's point, many other RPG systems that do fantasy have spell-points or spell-pools or mana points to represent spellcasting. D&D is one of the only games with the Vanican "Fire and forget" method.
Also, I think another distinction is that while Arcane is very; hocus-pocus in that, it follows much of the *out of thin air* (even with spell-components there is no reasoning behind why those spell components cause such a effect) trait. Psionics on the other hand while it is playing with the frabic of reality it is doing so in a somewhat understandable manner for many of its abilities, it is basically more scientific in lots of literature.
Thing is though, D&D isn't just one's person view of fantasy. It encompass many different ones, including ones that have science or pseudoscience. If it didn't many of the things we have seen in D&D since the very beginning would not exist.And that right there is where it probably comes to terms with people not wanting it in part of a fantasy setting they are trying to create that is devoid of science like refined steel, gunpowder, etc.
As for when- Psionics appear in an appendix of optional rules in the 1Ed PHB, along with rules for the Bard and rules for firearms and/or blending in elements of Boot Hill or Gamma World, as I recall.
Thing is though, D&D isn't just one's person view of fantasy. It encompass many different ones, including ones that have science or pseudoscience. If it didn't many of the things we have seen in D&D since the very beginning would not exist.
Like for myself; Psionics, trains, gunpowder and firearms, reinforced steel structures, etc, etc. all fit nice and neatly into my D&D. So why should my D&D fantasy setting be any less appropriate then another to exist?
If you don't want Psionics or gunpowder or anything else. Then simply don't use it, just like how I don't have Arcane or Divine magic in mine.
Edit: As for mana and spell-points, why can't it simply represent it being draining for the person? So while it doesn't physically damage them or the surroundings it does make them tired and unable to cast more spells?
As for psionics they generally follow in lots of literature the concept of it being very tiring and perhaps causing headaches, nose bleeds, seizures, brain aneurysm, etc, etc.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.