My wife and I also saw it in the same light when we first watched it during the original release. I think she likes it a lot more than I do, to be honest. I was also amused - especially after a rather outspoken individual recently insisted to me that no women like this film - to see an audience of about 80 percent teenage girls, many of whom were obviously fans wanting to see it in the cinema for the first time, at the recent rerelease screening I attended.
To your other points, it's interesting how some people take a very different view of this film (just glance around the comments and you'll see). For instance, some people think the very casting of Brad Pitt made the idolisation of Tyler Durden (by Incels, neo-Nazis, or whoever) inevitable. I'm not sure I altogether go along with that, but it's a point worth considering.
What I mean about the film lacking realism in the violence is that 1) none of these people strike me as people who'd thrown a punch in their lives (which I know you refute by saying they're meant to look inexperienced), and 2) some of the batterings, particularly the one applied to Jared Leto, would probably have resulted in death. After all, it only takes one punch to kill someone, if a blow goes awry (nose bone into the brain, etc).
All that said, I bow to your expertise, as I can't say I'm speaking from a wide range of bare knuckle or boxing experience. I've been in a couple of silly brawls as a teenager in which blows were exchanged, neither of which resulted in a clear victor, and neither of which are anecdotes worth relaying (neither were over a girl or anything interesting like that). All I remember is thinking how bloody idiotic (and painful) it was on both occasions. (I should also make clear that neither fight was started by me.)