Not able to answer the question, but do want to address the issue.
I would draw a sharp distinction between combats where the fiction is changing every round and those that are simple damage races with the fiction being basically unchanged each round.
Imagine a circumstance where you limited all action scenes in movies to 18 seconds, and if they lasted longer than 18 seconds you cut away from them to the conclusion. I think that's how an arbitrary limit on rounds would feel to me.
Now granted, I think there are many movies where combats go on and on without really adding to narrative, and simply exist for reasons of spectacle and frequently those bore me. But on the other hand, consider truly great cinematic combats like the climatic battle in Return of the Jedi where the protagonists are simultaneously fighting on three fronts and each of those three fronts has a narrative arc which throws action toward the other. That battle goes on for I'd guess 30 minutes of screen time and while the Ewoks beating up the Storm Troopers might be cheesy, it's not boring.
One thing that table top games tend not to do well is spectacle (or Sensation) so tabletop combat tends to be inherently less visceral than cinema while simultaneously taking longer to resolve. So while such combats can bore, in my experience they do not bore if during the combat the fiction is continually evolving in interesting ways.
I'm not hugely familiar with 4e combats, but from reputation they started to drag when the players ran out of options, were clearly in control of the battle, the fiction was no longer evolving, and yet several rounds of combat stretched out before the participants just to whittle down the hit points in a damage race the protagonists were obviously going to win.
I've had similar experiences in 1e with battles against large numbers of mooks, or in 3e against large numbers of low level undead, where it was clear that the foes couldn't significantly threaten the PCs and the combat devolved to the chore of whittling away the foes.
So for me, the question is not "Has the fight gone 3 rounds?", but rather, "Is the fight more resembling good cinema, or is it more resembling two 7 year olds playing the card game "War"?"
Trying to imagine a game were "combat is always over in 3 rounds", I can only imagine doing this if the game abandoned any attempt to simulate the events of combat, and instead staged combat as a sort of play in three acts where dice just provided guidance for the narration. Have you ever run combat in Amber Diceless roleplaying, for example? I could imagine a three Act rule applying to Amber Diceless. I have a hard time imagining it applying to any game which simulates a series of events.