All fights, all fighters have a rhythm, and that implies a certain pause. Drop a coin on the ground, pick it up. Now picture yourself sweaty and ragged breathing, arms shaking from adrenaline, various aches from blows received, and keeping an eye on the other person so they don't boot you in the face as you bend over.
About the only way viable, is if the other fellow is stunned, knocked down hard, or otherwise incapacitated. And then it's just sadism, hunting for your own tooth and trying to overpower someone who, presumably, doesn't want a tooth in their eye.
And no, not particularly memorable. Memorable, needs to be descriable in an interesting way.
https://www.youtube.com/watch?v=SE0oDPBslUs - "Starts with two men accidentally beating the shit out of each other while Cruise naps in a tub, ends with Cruise beating one up with the other"
https://www.youtube.com/watch?v=VwIIDzrVVdc - "Men beats his way through a horde with a hammer. And not even a big hammer"
https://www.youtube.com/watch?v=gBvOHpNhswo https://www.youtube.com/watch?v=iapVomK4eFA - "Hugh Grant & Colin Firth can't fight for shit. Intermission for mumbling happy birthday, and running away around a fountain"
https://www.youtube.com/watch?v=NXB6slJSbL4 - "Colin Firth CAN fight for shit, and murders the entire Westboro Baptists"
Yours, well. "Guy tortures a guy with a tooth". Not quite the same zing.