There's another question I think influences whether or not someone wants a past team: How old are the O5 supposed to be compared to Johnny Storm and Peter Parker?
Whenever I look at the Stan Lee era, the vibe I get is they were all more-or-less the same age. They were the "teen heroes" of Marvel, they all grew together. I think a lot of it boils down to it feeling awkward to make the O5 be younger than Peter and Johnny, which is what would happen if you make them teenagers and the movie comes out after 2021 (with Johnny I think the default assumption is they'll always base his age on Peter's then-and-there age, for obvious reasons).
You could argue they're younger in the current comics, but that's different. They're just new X-Men, not the founders of X-Men. Teenage Scott doesn't have to lead adult Storm because current teenage Scott is almost a different character, a second-gen superhero like Kamala Khan.
But if the movies start closer to a traditional status quo for the X-Men, where Xavier first recruits the O5 and then they carry on his dream, would it really be ideal to start there and then watch the new Spider-Man/Human Torch crossover? Would it "feel right"? To a lot of fans it doesn't and they don't know how to voice this, I think. It doesn't "feel right" the same way an age gap between Batman and Superman doesn't "feel right". Best word I could attribute to it is a "thematic inconsistency".
Regardless, a good compromise could be the Danger Room.
I hope that Bobby is the same age as Peter, and the rest no more than two years older than he. That would put them all in that college range. It's not too too hard to explain that they've been living normal lives, thanks to Prof X, since they were teens, and that leaves them young enough to be the new kids on the block without seeming like late bloomers, but old enough to have fully formed adult personalities.
I really REALLY like your idea that draws on a washed mission and the Danger Room. It really calls to mind Deadly Genesis, where Vulcan and Darwin's mission was a wash, and the whole thing about Giant Size X-Men is they come in BECAUSE the O5 washed on a mission. What if it was their first real mission?
Add in Xavier's telepathy, another cue from Deadly Genesis, and you can really have the O5 have this sort of non-experience doing missions. This dovetails with the audience's POV, where O5 X-Men missions didn't really happen in the MCU, it only happened for these characters, well... now that can be literally true in the story, and you can use the audience's disinterest in these adventures as part of the plot, deepening the connection to these characters as they come to the same conclusion that we all did: the previous iteration of the X-Men, despite its strengths, was ultimately a failure. And that's how you meta the hell out of a storyline to get the audience 100% on board a new train when they're still trying to give Oscars to the old one.
You think way to lowly of the general audience. They don't need everything spoonfed to them. With the right actors and script, you can establish the iconic, established X-Men as "big deals" in a couple of minutes.
On the contrary, I think very highly of them. The audience is too smart to think something that isn't worth the time of the filmmakers is worth their time. They're smart enough to understand when they're being spoonfed information and when they're being led step by step on a journey. They know the difference, and feel it, instantly, even if they can't describe it.
Give me examples of these 'big deals' because the only thing I can think about is loss storylines, where the loss is the big deal, and the loss is what's being explored, not so much looking up to someone. Or sometimes a kid will have a hero to look up to, and the lesson of the story is that the hero isn't really as great as they imagined, or "the real hero is you." Everytime something is set up as a big deal in a couple of minutes, it ends up losing/sucking/dying, because going from being a big deal to not a big deal is just as cool a journey as going from being not a big deal to being a big deal, like most (all?) superhero movies.
Polaris, Sage, Psylocke, Rogue, White Queen, Phoenix, Marrow, Storm, Shadowcat, Dazzler, Jubilee... Any of these characters could be as popular as Wonder Woman in a film.
As a team, definitely. Solo? None of those characters could bear a trilogy. Only the bolded could even manage a solo.
Because then when you do introduce Beast, Iceman, and Angel later on in a future X-Men movie.... the audience doesn't have to sit through origin stuff that slows the movie to a crawl.
MCU doesn't need that for enjoyment. They did Black Widow, Winter Soldier, Falcon, Scarlet Witch & Quicksilver, Vision, Valkyrie and more origins without slowing things to a crawl. If those characters had been off screen previous members of the Avengers, would the movies have been more enjoyable?