It's about verisimilitude, Danny. The avoidance of modern terms tricks the audience into thinking that, at least on some level, the imaginary world is real.
The way actual medievals would have perceived the word psionics is irrelevant. They don't play in our games. We care about the way the players, or readers if it's a published product, perceive the terms. It's the connotations that are important here, not the referent.
Proper use of language is a big deal in secondary world creation. Ask Tolkien if you don't believe me.
"Verisimilitude" is defined in the MW Dictionary as the quality or state of being "verisimilar"...which is defined as:
Verisimilar:
1 : having the appearance of truth : probable
2 : depicting realism (as in art or literature)
Don't get me wrong- I understand what you're saying about language and the willing suspension of disbelief.
I just don't suffer that in regards to "psionics," and reject the idea that how actual people in an era analogous to the typical fantasy setting would have used a word is irrelevant.
Within the context of a quasi-medieval world, any term that could have existed in that time- again, like "television"- is fair game IMHO, and satisfies the quality of verisimilitude, assuming that i
t is used in a way as a person of that era would have used it. This would indeed be "proper use of language," despite our having a different, modern understanding of the word.
So, "television" as having "far-seeing" or as an alternate term for a device like a telescope (which, BTW, was also called the perspicillum, conspicillum, specillum, and penicillium before telescope "won the battle") is fine, using it for the watching of entertainment on crystal balls in every house would be disruptive.
Similarly, a word like "Atom" has several meanings & modern connotations, but is quite an old term, and would have been used by an Alchemist or Natural Scientist. It might be disruptive, but it still has verisimilitude.
Now, the more divergent a fantasy world gets from our own past, the stronger the argument about verisimilitude gets...but only up to a point.
Middle Earth? While it has sciences of some kind- advanced metallurgy enough to make fine steels, medieval style fortresses, etc.- it also seems to lack some of the tech we'd find in a more closely analogous 15th-16th century world...like sophisticated lenses to make telescopes, clockwork automatons or gunpowder. Part of that can probably be attributed to Sauron's effect on the world.