The only time I can remember Billy ever being tied to the x-men was from the Sorcerers Supreme comic (and any other comic that used that iteration of him), where he was a member of the future team. Other than that, his only other Krakoa connection is that his brother is maybe dating a guy on their CSI-Krakoa team. And as I've said before, putting them in x-office hands is just asking for un-needed ooc power tantrums, possible genocides, or pointless relationship drama/love triangles, etc. At least under the Avengers office, they have star potential (especially with their MCU debuts coming up), under the x-office, they're what? A reality warper and speedster that'll get pushed to the side to let Wolverine have another man-pain comic. The best chance for them as mutants would have been their Magneto connection, but we all know how that is now.
I wouldn't mind a storyline where maybe Skrull and Kree mutants (those are a thing, right?) are allowed to tour Krakoa and Billy, with Tommy as a plus one (might as well pull him out of the toy box here), go with them to make sure they're safe. Then David gives them a tour, Anole fanboys like before, and then one of them spots the Wanda-propaganda and asks to speak to the manag- I mean, consults with Magneto for some extra drama! However, given the Outsiders vs Krakoa track record, Billy and Tommy would probably come off as assholes to make the mutants look better.