The martial arts closeness is definitely an interesting one, I think it's under recognized/discussed. A common beginner judo exercise is to have students aggressively jump-chestbump each other. It's a physical warmup but the main purpose is to break down the sense of personal space we keep in normal life. More advanced students don't generally do it, having learned to context switch into "grappling mode" at will.

I remember having one completely rough class where all got just worked, and during a break sitting in literally a pile of other students leaning back to back, helping each other rub out bruises, tape fingers etc and thinking "is this weird? this is a lot of intimacy, I barely know some of these people." There aren't many social contexts that have that level of physical interaction at all.

It can be strengthening or healing for sure. Martial arts schools are also a major venue for interpersonal abuses of all kinds. The required intimacy and the culture of deference to authority are perfect for it. Everywhere I've trained you have people who left other schools but you only hear ominous rumors of why.

Yeah it feels odd at first for sure. But like any other mammal, one of our social instincts is play fighting. You see it in kids with their roughhousing and horseplay, but as we get older it becomes less and less socially acceptable in most contexts. Socializing becomes less about having fun and bonding with people and more about observing unspoken rules and demonstrating that you know how to behave properly. There's nothing wrong with the latter, but you can't create genuine connections without the former. I believe this is why many people have the sense that their work friends aren't "real" and will fade away when they move on to their next job.

The abuse thing is certainly an issue, unfortunately. The "coach waiting until student turns 18" scenario is apparently so common in BJJ that it's practically a meme at this point, though I've been fortunate enough to go to a school where it hasn't happened, as far as I'm aware.