I think the short answer is that they do exist, in varying forms.

The Undisputed 3 reference of two distinct styles in a ring is a bit of a weird one, to me. That doesn't seem particularly modern at all. It's right there with Bloodsport and all its kin of "mixed martial arts" tournament movies of the eighties and nineties. Those movies grandfathered in the tropes of the genre at some of its peaks (Street Fighter II, Mortal Kombat, etc). What you're describing seems to be - to some extent - the modern brethren of the arcade era; Tekken, Dead or Alive, Virtua Fighter.

Going a step further (and using your example) you then have the latest slate of UFC games that play more easily with the UFC's brand of MMA and hard hits and submission. If you're motivated you can definitely play a version of that fighting style in games like Tekken or DOA, in the wider array of environments you're talking about. The only thing that's really missing is the freeflowing quality, which is probably territory more serviced by something like The Matrix game(s) (to use a dated reference).

Why isn't there a game that ticks all the boxes with the same tone you're talking about? I'm sure there's a laundry list of 80 percenters. At the end of the day it's a crowded market populated with some of the biggest brands in gaming. Games like this demand balance and do ultimately operate at their best when there's some sense of unifying principle; either stylized like SFII, sports influenced like UFC, or somewhere in between like facets of Tekken etc. When you try to take it into the world, that's usually when it starts to run up against more problems, which is probably why the popular approach is to simply the fight mechanics of games like that.

I think when you boil it all down, too many games do address what you're describing for a new player to make a confident entry. Maybe you can hit on something more specific you think is missing, though. Maybe it's not just an issue of tone.

I've kind of wondered the same thing. I think it'd be cool to see a fighting game done sort of like a hybrid Tao Feng/UFC game. Where a lot of the mocap, and actors where actual big names from Hollywood. Like Tony Ja, Jet Li and Jason Statham.

Jason Statham? Really?

Jason David Frank - oh yeah, now you're talking.