not well versed in the period, but from my understanding Vince Sr was concerned that turning Billy Graham babyface was a bad idea because he had long hair and he thought it was a bad influence on children to have a counter-culture Proto-Hogan as face of the company, so he dropped it to a Backlund, who was obviously a more clean cut, 50s American kind of deal, as a guy with Long Hair myself, this wouldn't be a big deal now, but many people, especially back then gave a shit about that, just kind of how it was
I can't say I've ever heard this story at all. This shit about Graham turning face didn't start until he suggested it in his book years ago, is Graham's revisionist history in the wake of Stone Cold Steve Austin. Before Graham's book, i'd never previously read, or heard of a scenario where Graham suggested to big Vince that he be turned face. That sounds like something Graham's biggest dickrider, Meltzer, would push as legit.
The fact of the matter is, Vince the elder, wanted a clean cut, white, white meat babyface in the Jack Brisco mold, as he was expanding the WWWF out to the suburbs, where a spic like Morales, and a wop like Sammartino, or a roided up hippie like Graham, would be a harder sell to suburbanite kids. He also wanted someone relatively new, who didn't have any personal demons, could get over with the fans, and most importantly, was not going to throw their weight around about bookings and payoffs like Sammartino did.
Once Backlund was decided upon in 1977,
then he chose Graham to keep the title warm while they built Backlund up on WWWF TV. it was merely gravy that Graham was able to get over so well at the Gardens (Madison Square and Boston).
Beyond that, Graham just was not capable enough in the ring to wrestle like a babyface. And despite what Graham and that faggot Meltzer would have you believe, if you were a babyface in the WWWF in those days, you were expected to wrestle like one. Hell, even Brawling Bruno, didn't start unloading on heels until they "made him angry" by cheating.
EDIT: sentence clarification