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.
That is probably one of the major reason it is not part of the core...exactly...
Psionics doesn't fit for everyone, and they don't always want it. The main question is how to make it fit. D&D cannot be a catch-all system for all types of gameplay. That was a big downfall to 3rd and the d20 system. It was too big and allowed for too much that it couldn't hone in on anything.
Sometimes you just have to let another game do things. You cannot make everything fit, like adding mammals eating marbles into Yahtzee. Maybe those hungry hippos eat the dice instead of rolling them...it doesn't always work combining too many things.
As far as the mana points, you are basically making something akin to Vancian psionics. You have these power points based on physical strengths that do what to you as you use them? Can it danger you to use them all and then end up with prone character prime for the picking that other characters will need to heavily gaurd rather than attend to their own duties.
The system just cannot support everything, and that is where it is losing ground by trying to. It is ok to make a new system like 2nd edition tried, but still forcing it all into the same package.
Hasbro doesn't just make one board game, they make a diverse assortment of games to accommodate the largest audiences possible. D&D should take that approach and make different RPGs for the different styles of gaming. They don't have to include everything just so you can say you are playing D&D. It is ok to play a medieval fantasy RPG that isn't D&D, and likewise ok to play a to play a Lovecraft inspired game that doesn't take place in D&D.
Too many of these things are really choking the system throughout the years, and there comes to a point where you have to stop choking it with trying to make everything fit together or you risk killing it. You need to be able to make the best use of what is there, and then accept it is ok to make/play something else rather than falling in love with the name.
Psionics can have a game themed around them, but it needs to be made and promoted.
While getting away from Vancian magic in the form of powers with 4th edition rather than memorized spells as such, why fall back into the same trappings with a mana pool for psionics?
Then you also have to worry about dying from perform your duties during the game? That is where psionics falls apart at the basis of creation to fit within established areas of D&D and the way things work within it. You eyes start bleeding and can no longer see, so what good are you for the rest of the battle from overuse of psy abilities?
And people said the fighter had problems and power/usefullness envy!