The X-men haven't been in the "spotlight" since 2000, in fact even when they were more prominent like in the 90s they still were pretty insulated in their own corner of the MU. Outside of event like Onslaught they didn't get very involved with the other franchises.
Being "the favorites", which they aren't, isn't the problem, actually I don't think the editors like the X-men at all, they are pretty much stuck with the comics because they sell. But they started to build another franchise using all the X-men tropes on them and pretty much trying to sideline the X-men by cutting down the number of titles among other things.
The X-men and the Inhumans have been coexisting since the 60s actually but in this highly corporate enviroment in Marvel I don't think this could be the case anymore, the push of the Inhumans didn't go as well as planned but they will keep going with it, and honestly with the time they could pretty much succeed which will mean they wouldn'thave any reason to keep publish a franchise they can't get 100% of profit, yeah pretty much the success of the Inhumans means the downfall of the X-men.