Destiny's Child - "If" - Here
I think it really comes down to the fact that the X-Men as a team are the franchise.
The Avengers are a bunch of smaller franchises put together (Hulk, Iron Man, Cap, Thor, plus a lot of smaller characters). Which is why those members can carry their own book, because they are a thing all by themselves. They have an identity outside of the Avengers.
Most X-Men can't hold a solo book because you are only getting a fraction of something. Wolverine is the usual exception, mainly because he sort of became his own thing decades ago.
"That's a very nice school you have here, it'd be a shame if someone dropped some Sentinels on it"
Storm is barely even the most recognizable X female and probably holds onto the spot due to the writers inadvertently sabotaging the competition.
I agree about Schism however. It wasn't constructed along any sort of generational line or anything besides random team A and random team B.
The FF members don't have the capacity for believeable independent action. Writing the idea that Sue for instance is going to start flying solo on her downtime would require a major redefinition in the character's relationships.
It wouldn't take much of a leap at all to move an X character off on their own in the same way DC franchises the Batfamily members. Its really as simple as getting across that Wolverine(their model on how to do it) is someone who doesn't/wouldn't live at the mansion/school whatever, and that being an X-Man is a set of ideals and not a job i.e. Avenger.