I tried looking in the books I have and none of the main characters (prof X, Jean Grey, etc) I can't find anything that says I can't do it, but has anyone else done this already.
All of this, of course, when treading away from the rules as written, depends heavily on the GM and GM approval.
I've seen fan-made characters who have Mastery of Psionic Energy (perhaps the one closest to canon would be versions I've seen of Nate Grey/X-Man). Depending on the degree of utility/versatility, the Mastery could warrant anywhere from +1-+3 to CL (using Mastery of Magnetism or Mastery of Four Elements as guideposts in that regard). The big question I would have as a GM pricing such an action is what you'd want such a Mastery to accomplish, what would you think create/manipulate should be able to accomplish, what "immunity to element" would entail, what free options a force blast would grant, and so on.
I personally see no problem with that whatsoever, and I would not charge more for it at all. To me, that's more of a flavor thing than anything else. Just like how I wouldn't charge higher for a mutant like Forge whose power is Inventing VS a 'normal Inventor' like Stark. Technically speaking, Apocalypse's powers are psychic in nature, since he 'psychically alters the molecules in his body' to be able to shapeshift into whatever, and yet, at the end of the day, his power is Transform Self Unlimited. It simply has psychic origins instead of some sort of 'basic' metamorphosis ability.
I've done this several times. I just change the names a bit. For example, a psychic Mastery of Fire I call Pyrokinesis. Ice would be Cryokinesis, and so on.
Nothing is impossible, it just hasn't been done yet.
I feel like there’s a character in the Avengers supplement that has something along those lines...
I think it was Justice.
You could definitely do it. Telekinesis could be an option, as well as a force blast. The force field option would fit, and you could buy flight at a discount. If you're talking about telepathy, probably not. But if you take telepathy, you can get telekinesis with a discount, as well as free mental defense. Force field get's a discount if you take telekinesis, and it isn't that expensive to get an intelligence bonus on telepathy and telekinesis. While you're at it, you might as well add psycho-centric power template.
So I guess there's isn't really a need for a psionics mastery.