When is the last time that a major program in need of a coach, men or women, said: "Huh, I wonder if there are any good coaches
in Div. II?" USC just hired a new men's coach--nabbed him from Arkansas. Arkansas, now needing a coach, tried to hire the well-respected coach
at Ole Miss and then the coach at Kansas State. They declined, so Arkansas pitched Calipari at Kentucky--and got him! Their ADs didn't say, "Ah, to hell with established winners, lemme see if there are any good coaches with 1 year of mid-major experience." Nobody does that. It is virtually unprecedented.
If Barnes retired tomorrow, would White say: "Hmmm, I've got my eye on this guy who killed it in Div. II and just had a super year at Appalachian State. He could be the answer." Would he? Would the men's fan base be happy with that? No, they would not. And I doubt White would do it--but knowing him, I wouldn't rule it out.