They can try. I remember when Nine Inch Nails came out with the song "Closer To God", they did manage to get some airplay with an edited version of a song that would otherwise drop the F-bomb in every repetition of the chorus. More recently, there have been a couple of songs that just recorded alternate lyrics that replace the F-bomb with something more acceptable. CeeLo Green's "Forget You" (originally "F... You") comes to mind, as does "Tonight I'm Lovin' You" by Enrique Iglesias. Most recent would be "ABCDEFU" by Gayle.Yeah, when every 'chorus' or hook contains an F-bomb and the listener already knows the actual lyrics, it's simply not worth the effort.
The clean versions of several of these songs have done quite well.