Let me reframe this, going away from D&D's 6-second turns...
Oh, I don't think the length of the turn really matters. We can stick to Vampire if you prefer. The point is that Vampire is set up to run combat as a series of events. One thing happens after the other. If anything, it's more granular and less abstract than D&D running it in an intuitive fashion, because it has a very GURPS like attack, active defense, passive defense, apply damage sort of procedure.
Again, I can see systems where this might work - Amber Diceless is one I've already mentioned. If you want to run a combat in a system where the combat outcome revolves around narrative currency, and the participants work together to narrate the combat, then a 'three act' rule for a combat might be fine - opening, rising action, climax. Two skilled players could probably produce something like the duel from "Princess Bride" under these conditions.
In practice, I don't find most movie combats - especially modern movie combats in this era after movies like The Phantom Menace or The Bourne Ultimatum - to be particularly tightly paced. Most to me are a boring drag, and I really don't want many action movies any more because of it. What you more often see is fighting not as means of telling a narrative, but rather as a means of spectacle - showing off special effects, showing off fight choreography, etc. You watch many modern movies for the same reasons you watch a Jackie Chan movie - the stylized lengthy combat scenes are the meat of the movie.
But fundamentally, you've "reframed" this by attacking my movie metaphor and other details, yet I don't see you really threatening my central point - which is that a combat in an RPG continues to be exciting so long as the fiction continues to meaningfully evolve. That is to say, during the fight, is something interesting still happening? Is the fight tense, exciting, fun to imagine, producing dramatic moments, or shining moments of awesome? Is the fight moving across terrain? Is the fight producing new goals and twists? Are new things happening from round to round, and new complications being introduced? If you do that successfully, the fight won't be a grind, regardless of whether it took 3 rounds, 6 rounds, or 12. The trick, or problem depending on how you look at it, is that this is much harder to do in a player's imagination than it is to do in cinema.
If you have an encounter that is going to go 3 rounds, and then already be a grind, then there is definitely something wrong with your encounter design that arbitrarily ending the battle won't fix. Perhaps if you wanted a plot twist, escape, or other bit of storytelling, you should have designed possibilities like that into the encounter in the first place, rather than going, "Gee... three rounds have gone by... this is a drag. Perhaps I ought to invent on the fly some away the fiction has meaningfully evolved." So in a very real way, when you say, "Keep the fiction evolving" you are agreeing with me. I totally would agree that, for example, a fight that potentially evolves into a chase sequence is a well designed encounter, or that a fight that potentially evolves into a social encounter is well designed, or a fight that starts out with one tactical problem (stop gaurds from sounding alarm) but can evolve into another one is well designed. What I don't agree with is using railroading techniques like arbitrarily cutting off the action (a "handwave") is a satisfactory way to get there if you are running some sort of process simulation combat.
Fights get grindy when you have uninteresting terrain, uninteresting goals, and uninteresting foes that do the same basic thing round after round, and winning is a matter of simply eroding hit points without making any real choices.