I can't argue that previous solo runs with Storm, Rogue, and Kurt were massive successes*, but it's simply not because these characters don't have rich backgrounds outside of being X-Men. Claremont gave them as much, if not more, dimension as Wolverine in those early years.
I respect being skeptical about the Phoenix and Storm runs lasting long, but they're undeniably very popular characters. A-listers where Logan is an S-lister. And popular characters just need to be in the right hands with the right push at the right time to do well.
*Ewing's 3 year run in the Krakoa Era has been dedicated to Storm solos in all but name
I think I probably wasn't clear enough but the character backgrounding is just one element really and more of a jumping off thing. The core issue with X-Solos is really about fanbase expectations and how they're used to digesting these characters. Even though the premise is nominally based around school, the core draw of the X-Men, New Mutants, X-Factor, Excalibur, Gen X, etc, is really in being found family and the organic connections and relationships therein. And I think that's a big part in why solos have had so much trouble breaking out versus the Avengers or Heroes Office titles (aka: work friends). These characters are defined within the ensemble and that's just what people seem to want really.
And I should probably make clear, I hope I'm wrong about these solos lasting. I think they're interesting premises and Storm especially could still be an ensemble title depending on her staff (Sunspot? Callisto? Bishop? maybe some deeper cuts like Vange Whedon or Sabra? ... or maybe not Sabra, lol). Throwing Jean into cosmic is a good approach too with so much room to explore and really go any direction and still with some good X-Connections with the Shi'ar, Starjammers, Brood, etc. I'm hoping for the best here, just bracing for the usual.
You make a good point on X-Men Red, though I think Magneto shared spotlight pretty equally in the first half, and this isn't even really a new concept. X-Men Legacy was built around this premise, a solo character focus steeped in continuity but holding the "X-Men" title basically to mitigate risk and trick the fanbase into actually buying it. And it did have 3 very well regarded runs, two with Carey (Xavier, Rogue) and then Spurrier's X-Debut (Legion). Actually Claremont's 2014 Nightcrawler series (which I liked a lot but ymmv) was also originally planned to be a 4th Legacy volume.