The most unrealistic thing about Star Trek is the part where there are hundreds of nerds lost in space and nobody uses the Holodeck to host a fucking dungeons and dragons game.
Still, as odd as it sounds, the thing that also makes me think the most is that no classic/medieval/renaissance societies thought of doing anything similar to D&D, at least not on the sense of wargaming and more on the sense of roleplaying with a central narrator.
Imagine if any of them ever knew WoW. or FFXIVOMFG IT'LL BE "SHUT UP AND TAKE MY NON-EXISTANT MONEY" LEVELS OF YES