I think Brad has gotten pretty good at production in the time that he wasn't focusing on guitar during ATS and LT, so I don't see why he wouldn't be working on some stuff on his own like Mike often does. Other than Brad being lazy or uninterested, he's pretty close to Mike's level, if not better in some aspects like playing guitar. He could write some good stuff if Mike and Chester aren't readily available.
Or, you know, the other three guys in the band could write some stuff too.