They should be placed in some sort of toxic-waste containment vessel of an optional module, preferably associated with Dark Sun, the only D&D setting in which they remotely have anything of value to add - if not in a Gamma World or other sci-fi/science-fantasy adjunct to D&D, along with mutants, laser pistols, and other things that have just as much right as psionics to be in an heroic fantasy RPG.
Yep. Sci-fi/Fantasy are often placed on the same shelves at bookstores, but that doesn't mean Mr. Spock should be mind melding with Frodo to keep The Ring from controlling him.
sci-fi, pure and simple. Having an alien race that vaguely alludes to celtic mythology and putting horses on the cover doesn't make your time high-tech time-travel epic /fantasy/.
Absolutely not. OTOH, it should use the same mechanics and progressions as other Sources, rather than being abberant for the sake of being able to put 'power points' on the character sheet, or being another clumsy bolt-on 'option' that serves only to add to the complexity of the game.
I disagree with your points, however it is all a matter of opinion so obviously this works for you.
However, a counter example. First a clarification on why I believe they can exist side by side.
You can consider pisionics to be the "sci-fi" version of magic. Fair enough, so do I. See for me like in many popular stories, magic can ebb and flow, go away for an age, return etc. But psionics, being "reality" based would still exist.
True, both are similar (underlying sources of reality changing effects, etc.) but the approach is different.
To my example, in 1st edition, many powerful monsters and powers had psionic defenses. So I created a backstory where psionics (the will) was the most powerful force underlying the cosmos. It was the power used by the gods to alter reality. Divine power was what they granted through belief (here's will involved again). And magic was the tradition of the arcane that approached altering reality through a science like tradition of rituals and spells.
Convoluted? Typed into a message board sure..

In play, fairly elegant.
Psionics worked in dead magic zones. Mind Flayers feared. Dragon Kings working on becoming gods through magic psionic mixes. Psionics hated and persecuted because the gods don't want it spreading and wizards dont trust it (burn it! burn it!). Wild unexplainable talents in certain people (danger sense etc). Monks altering their bodies through willpower but seemingly not magic.
And naturally in my campaign, the "Ancients" were psionic with weird unexplainable powers that were forbidden. (Because they were working on ascending to godlike creatures or were descended from the original race that built the cosmos).
Lot's of examples where using both and keeping them different work for us, both in fiction and dnd lore...but naturally this could seem contrived to others.
But it works for us.
/on topic
It was originally an appendix, so I would be cool with it as an add-on (love Green Ronin's Psychic Handbook) but I do want it different in flavor and play.