"Power defending" is best done with Interceptors, not AA. While AA divisions will continue to do trivial damage to the bombers long after provincial AA has been completely wrecked by the first couple of raids, they're not enough to really stop the bombing on their own. A wing of 3x or 4x Interceptors can ground the bombers for repair for weeks at a time.
Repair is at a rate defined by Infrastructure, so spreading your 10 factories out across 10 provinces means that all 10 are repairing simultaneously, rather than sequentially. It does mean that you may need to defend all 10 locations, and boost the Infrastructure in all 10, rather than in just one. Against the AI, the defense is not problem, because the AI will tend to hit the same one or two provinces over and over every time they repair above some threshold.