I suspect that "psionics" have entrenched themselves in Space Opera is that just like spaceships cruising the Galaxy relatively quickly or time travel, there was an idea in the 1940s-1960s that these things might just be possible. ESP was taken quasi-seriously at the time and it seemed like further technological development might allow it to become mainstream.
Asimov's Foundation, for example, has ESP develop as a consequence of scientific development, specifically the refinement of psychology. Telepathy is extremely refined psycho-analysis of tiny movements of the face and body, and mental control/hypnosis is just very refined brain fuckery. Both are almost certainly not possible as psychology is understood today, but as it was understood in the 40s it makes a lot more sense. At least until Foundation's Edge was written, then any veneer of scientific ESP fucks off and dies.