If we sign Burnett, he'd be the #5. No one's going to beat him out even, in the unlikely chance, someone out performs him. Detwiler pitches will out of the bullpen and he's function as the #6 starters. This is precisely what the Tigers did with Smily last season.
Pitchers get hurt. You're best served by having as many options as possible.
I just read on mlbtr that the Dodgers are going to sign Paul Maholm to a minor league deal. The Dodgers get it. They've already stacked their bullpen with established relievers and they're giving themselves options in the starting rotation.