As I have seen/read/experienced, roosters housed with their hens tend to have their favorites and those are the ones who end up with bare backs. From what I see in my own flock, that is quite believable. I see the roosters on those hens with bare backs a lot during what I call breeding season. In the same pen has been some hens that have a good coverage of feathers. I had one Buckeye rooster to 9 hens last year and still about 6 of them were bare backed by summer. I am making hen saddles to help reduce the damage like I have seen in the past. They do help, but they don't always stay on.
I wish I had space during breeding season to keep my cocks separate from the hens, but since I don't have that many pens, and if I were to swap the boys around like you suggest by putting them out with the mixed flock, I would have bloody roosters all season, if not a few dead ones from fighting. Since I have a few breeds here, some methods just are not practical.