The real time aspect may be part of the problem.
It is almost trivial in real time on a game to zip around all over a map in a way that would look pretty "stupid" if it was filmed for a TV show.
In D&D, the party just doesn't move that way.
Hadn't thought of it like that but yes you're probably right. All that strafing, jumping, running away to periodically hack at a pursuing enemy, it does feel, as you say, lacking in verisimilitude.
And a good GM can make a turn based combat feel more like real-time, or at least give it that illusion, by the manner in which they present and relay the actions of the combatants.