Yeah, I would hate for the X-Men to be integrated into the whole MCU shiz. They're far better off in their own separate universe, where there's humans and there's mutants, and that's it.
I like how you can sort of 'ground' mutant superhuman abilities to an almost-real world, without actually taking much of the utterly bonkers fantasy out of it all. In the sense that on Earth, the animal kingdom and plantlife already have a bunch of absolutely fucking mindblowng evolutionary adaptions, and stuff we still don't understand about intelligence and nonverbal communication, so genetic mutation is a wonderfully simple and elegant explanation/non-explanation for these fantastical but still somehow familiar and recognisably mortal (even when they're not!) beings.
There are seemingly very few ways to actually kill Wolverine, and yet, despite all signs pointing to him being practically invincible, we still have the sense that he can be in danger, that he could be bravely sacrificing himself here, that his lifeforce could be extinguished in some way. That's quite clever, that through a tacit understanding of his world's rules, and probably in combination with his very human flaws and relatability, he never really becomes a distant boringly-indestructible god figure. The whole mysterious-but-natural-sciencey genetic mutation thing somehow seems to help do that with these beings who are, to all intents and purposes, gods among men.
I've always loved the idea that there are plenty of absolutely fucking useless mutations around in the X-Men's world, probably more of them than there are truly useful ones, and it's all very trial & error but still ingenious, just like nature is. A lot of the useless ones just die out without much fanfare; indeed their mutation may in itself be a fatal condition. It's a genetic lottery much like the one we see play out in our own world, but where the most beautiful are instead shapeshifters, the most intelligent are telepaths, the strongest are made of 'organic steel', and so on. It's such an interesting collective origin story, the barely-understood emergence of a whole new human species, and it's a brilliant character-building device in that you can explore an individual's origin with their own unique abilities, while having that zoomed-in developing story serve as a microcosm for the development of mutants as a race. It helps so much having that play out in its own separate universe, away from all the radioactive-spider-bitten-teenagers and alien Vikings and what have you. It's just so much tidier.