The heel turn was, in my opinion, a result of the Orton face turn, something that was not originally intended. A feud between the fromer Rated-RKO members was obviously something that was going to happen sooner or later and I believe WWE wanted to do it following the Edge/Jericho feud with Orton as the heel. That went out of the window when the fans refused to accept the idea of Ted Dibiase's face turn, forcing the Randy switch instead and that forced a number of other changes. On top of that, Edge wasn't in the kind of condition necassary to pull of his face moveset convincingly so reverting to heel made a lot of sense from that perspective.
Edge, as the Rated-R Superstar, can really only do so many things in a PG environment and still seem relevant. That's why I enjoyed it so much when he abruptly turned on Orton and just went back to his roots. His promos (over the next few weeks) just felt genuine.
With his first face run, Edge didn't really get the chance to do anything. He had a grudge with Jericho, and that's all it revolved around. Beyond that, he was given the "Spear" chant. And that's it. Nothing more, nothing less.
He couldn't break rules, be a badass, and live up to the Rated-R Superstar moniker. The feud wasn't about that. It was a personal rivalry, built around the serious issue of a career-ending injury.
Once that feud was wrapped up, Edge went back to being a heel. So they never really experimented or tried anything else to help him fall into the role of being a top babyface.
With the "eliminating the stupid things in WWE" campaign that Edge began a month or so ago, they had their ticket. It wasn't the most creative idea or anything, but it was just basic and realistic enough to work.
It's perfectly believable that Edge's character would've become impatient and furious about the Mystery GM, the Swagger Eagle, and other things he sees as "stupid." It's a feeling that people could relate to.
By that definition, it makes sense to be the motivation of a babyface.
Well whatever the reason they are doing Edges face turn a lot better than his last one. Much less crowd pandering and generic promos. He's still an interesting babyface. Odd that those only exist on Smackdown.