What you describe there is the standard X-Men dynamic, as created by Chris Claremont.
Precisely my point, yes. The problem is, because ALL superheroes are now persecuted, and not JUST mutants, that sliver-thin shred of "social relevance" that mutants once had is utterly gone. Without the metaphor of an oppressed minority to back them up, all that mutants are, in the words of Howard Chaykin, is beautiful people who have problems that regular people only WISH that they had, and really, wasn't that one of the criticisms that X-Men fans used to level against Avengers fans, before Bendis, back when the Avengers were the "country club" of superheroes?
When was that not the case? What else is there?
The Claremont dynamic was good for its day, but it needs to be shitcanned - completely, utterly and for all time. Morrison's rendition of mutants as their own subculture, within a larger society, was actually a step in the right direction, but even he wasted too much time on grade-Z-level imitations of Claremont soap opera plots.