The Avengers, Spidey, FF, etc. have always been meant to be the core of Marvel. It's when they lost sight of that and tried to make the X-Men all things to all people that the X-Men suffered for it creatively, along with the company.
The X-Men need to be unique and colorful in their own way. They should not be disenfranchised as Ike Perlmutter did to them through the last two decades, but they should not be overpowering the company line and treated like the Avengers as they were in the 90s, blanded out. They are meant to be a courageous reflection of minorities and different people in our own world, a powerful living metaphor.
I take zero issue with how the MCU and Marvel have made the Avengers central. It is the way they have always been treated in-universe and now the company reflects that again. I am just glad it is now no longer being done at the expense of the X-Men within the comic line. It is not a competition.
And that's bad... why? Power Pack has always been close to the X-Men, and I'm not sure if they had any connection to the Avengers. So that's why I wouldn't want MCU Power Pack to force one. Also, the Avengers have been the leads of every single big line-wide event for a while now, during the X-Men dark age, so now that we have the X-Men treated well again, why not mix it up?
Why on earth would Power Pack not be fans of the Avengers, like virtually every child and/or junior hero in the Marvel Universe? Yes, they like the X-Men too, so what?
I think a lot of the distance started when Claremont became too busy with X-Men and its spinoffs to write other books, and the editors mostly concentrated on the X-titles. Writers and editors usually find it easiest to do crossovers within their own titles, which is how we got Misty Knight as Jean's roommate and Iron Fist fighting the new X-Men over a misunderstanding. But coordinating between different writers and different editorial offices is hard and often not worth what it does to both writers' stories. Something like this happened in the late '80s when the Avengers and X-Men offices got together to do the X-Men vs. Avengers crossover, where the last issue had to be completely re-plotted because of editorial/writer conflicts over how Magneto should be portrayed.
Then we get to the early '90s when the X-books are so huge that they are almost like a publishing line in themselves. Bob Harras was also writing "Avengers" at the time, and he did sometimes cross them over, but not very often because his needs as an editor were different from his needs as a writer (eg an Avengers/X-Men crossover was announced that would focus on Magneto as Quicksilver and Scarlet Witch's father, but after "Fatal Attractions" took Magneto off the board, he was replaced by Exodus and the crossover turned out to be weak).
So it is true that if someone was reading only the X-books they wouldn't see much of other Marvel characters, but I think that's largely because there are too many X-books for the editors to work on anything else. If the same writer/editor team were doing X-Men and Avengers you'd probably see more crossovers (not that I'm advocating that).
Another thing that really bugs me about how these people speak of it as an offshoot, and want the X-Men jettisoned to their own universe so that the mutant racism can "make more sense", is that I feel like these people are primarily MCU fans and only feel the X-Men aren't relevant to the lore by way of movie rights. The people who speak of X-Men this way act like they're not a true part of Marvel, just some sub-series that's loosely connected and disposable. "Less Marvel", in some way. They clearly don't know their history in regards to comic books.
While it was made famous and reinvented by Chris Claremont and John Byrne, it wasn't first created by some obscure names lost in history. The fact is that the concept of the X-Men was first thought of and written by Stan "The Man" Lee and drawn out by Jack "The King" Kirby. As in, the two most important people in Marvel history. That's as "Marvel" as it gets. Literally, I don't think it's possible for a comic to be any more of a true Marvel creation than that.
"Less Marvel" is just plain wrong. Though, funnily enough, it actually echoes the ideas of mutant racism in a different way.