The Vampire mechanic is "keep going if you are having fun". So it's really "stop when it becomes a grind - but go at least three rounds'.
I think that addresses the rest of your points.
I don't know about ninjayeti, but that addresses all of my concerns. Initially I thought the "three round combat rule" meant FIGHTS MUST END AFTER THREE ROUNDS which would have been an unspeakably crappy game mechanic (except perhaps in a very niche game designed around a very niche concept that fits that rule).
It's weird yet not unexpected that there's been so much discussion within the D&D frame in this thread about the new Vampire. I have not played a lot of WoD and the WoD that I did play was ages ago when I was a teenager and EVEN THEN as a teenager--the height of the appeal of the Trenchcoat McKatanas style of VtM play--combat was not particularly common. Now, as for D&D...I've heard many a player say that fights virtually never last more than three rounds anyway, and it's not usually said like it's a good thing. It's not that players want longer combats, but in various editions of the game (including, I think, the current one) certain abilities and parameters will never be relevant within that time-space. In 5E, a duration of one minute might as well be a duration of forever because I don't think I've ever seen a ten turn combat (not that I'd necessarily want to). In 3.X frequently various spells or spell-like abilities had a duration of Caster Level rounds. Because combats lasting more than three rounds are almost unheard of, this meant that there was no meaningful difference in duration between a spell cast by a 3rd level character and a spell cast by a 15th level character.
Because I have Legendary Resistance 3/Day, I will
choose to succeed my Wisdom save against launching into my rant on how painfully idiotic the 3-6 second combat turn is right here and now. I will say that I have come to the conclusion that the combat turn should really be, at a minimum, 10 seconds, for a ratio of six turns to one minute, but I won't justify that assertion because I think then I'd fall into the rant I said I was avoiding.
I don't know that I'd go so far as to say I
want longer combats (in rounds) in my D&D, but I do know that the most fun D&D combats I've run have all been the ones that ran well over three rounds. That said I'm broadly in favor of the thinking on this new Vampire rule, but in the D&D context I don't think it needs a rule as such. If after three rounds the party is getting its ass kicked, the logical thing for the party to do is to run away. If after three rounds the enemies are getting their asses kicked, the logical thing for the DM to do is to have them runaway or surrender, assuming they're not mindless--even the dumbest orcs, goblins, bugbears, troglodytes, whatever, are smart enough to realize that hey, 12 seconds ago there were ten of us and now there are three of us, let's GTFO (this is also why I've never felt a need for morale mechanics; a glance at the board state is usually enough to let me tell when the enemies would lose morale and retreat). If after three rounds the fight is undecided then play on, play on, play on!
Oh, and the last thing I wanted to say is...while I definitely understand, as a game designer, the desire to make fights resolve faster, I think there's an external limit on what you can accomplish with the actual system and mechanics. No matter how much you simplify and streamline, you are still going to run into the fact that many players are very slow. If your game has meaningful choices for PCs to make in combat--and honestly a game that doesn't probably shouldn't even
have combat--a certain portion of players are going to fall into analysis paralysis and slow things way down, no matter how many times the DM has asked them to PLEASE have their decision ready when their turn comes up. A certain portion of players will struggle with the mechanics of any game system that is remotely new to them, and that too slows things down. A certain portion of players will have two, or three, or five, or ten, or fifteen questions about the battle situation--at least half of which you have already told them the answer to, they just weren't paying attention. And finally some players are just jerks and slow down combat with dumb arguments. I don't think there's anything to be done about any of this, I just don't think combat in an RPG is ever going to run at anything close to the ideal speed it would run at in a perfect world (which I'd say is probably 1-2 minutes of real time to each full combat turn) unless the players have been selectively curated. My only real point with all of this is that there is only so much MECHANICS can do to "make combat fast".
Those are my random thoughts.