if villain is holding hands that beat us such as Ax or smaller pairs then i dont think CR will accomplish much since he'll check a ton back for pot control and a cheap showdown. you get the odd bluff or semibluff that might fold in this spot but those are hands we'd likely make fold by barreling here anyway including those hands that are ahead of us.

are you really going to bet flop and then CR a hand like KK or AA here with a bunch of draws out there? (unless you have some read that villain always raises draws on this flop.. and you're not too worried about giving free cards when you have the goods)