A strong core is critical for transferring force through the legs, especially in initiating moves. But I don't see that as the whole story with getting over roof problems. Extending movement up from the legs through the core has the effect of lifting the torso higher, bring the climber's COG into a potentially more advantageous position with respect to the roof lip and/or holds above the roof. So what we're really talking about is technique.

I'm not a tall person, but let's say I'm climbing like one in so far that my feet are still on holds on the back wall under the roof. As I move up, I'll try to bring my hips in close to the roof. It's easier to then look downward past my legs to see where I need to re-position my feet. It also seems easier to pull my torso up and in and hold a lock-off on one arm while reaching out around the roof with the other. The post by AnthonyB also brought this up and included some other good ideas.