I like psychic powers.
I think a LOT of the hate, confusion, and disike that psychic powers receive in D&D was their initial, and admittedly flawed, inclusion as "psionics." The term itself is problematic, being from science fiction, psychic powers brought about or amplified through bionic implants, thus "psionics."
Of course this was also back in the proverbial day where the "fantasy" genre itself was not "fantasy" as we think of it today. It wasn't just elves and magic and dragons. "Fantasy" pulp novels included things like science fiction, action/adventure (like Tarzan or Indiana Jones), gothic-y horror stuff, even detective series...and lots of it thrown in a blender with elements from any of them in the same story.
So, we got "psionics" as the generic D&D term for psychic powers. Problem for people #1.
Implementation was thoroughly obtuse and confusing to implement. Problem for people #2. Though power points and other, non-D&D, systems have greatly improved their mechanic accessibility over the years.
Many "Psionics" do what magic does. ESP, Clairvoyance, Telekinesis, Pyrotechnics...all available as spells. Are psychic powers "magic" or something else? Are they a different kind or way of working magic? Is that gypsy at the carnival with the tarot cards a "magic-user" or a "psychic"? Story issues. Problem for people #3.
All that said, I like psychic powers. I incorporate them into my homebrew campaign world/setting and game rules (using a power point model similar to spell levels, but more "at will"). They are not "magic" in the arcane/divine/natural, exterior power source, sense. Psychic individuals in Orea are your Jean Greys and Professor X's. They have "powers" not "spells." Internal mental energies that are significantly higher/more pronounced than your normal person. They aren't "magic-users" (though could be in addition to their mental gifts, or warriors or rogues or priests) they are "psychics."
Most belong to, and are sought out for, a pseudo-religious organization of psychics for their own protection and training/expansion of their powers. In some lands they are trusted, even revered, counselors. Some lands view them as "possessed" by evil spirits/forces, in need of hunting down and slaying before the evil can release itself. And there is a certain cabal of [evil] wizards who seek them out for "research"[including dissection] to ascertain the cause of their powers and how to acquire such power for themselves...independent of the restrictions of spell use.
They are, of course, exceptionally rare and generally only used as NPCs...I only recall 1 player ever being one as a class.