I suggest you look at your rooster's legs and feet. Look closely at the spurs. How many are there and how sharp are they. Then look at the claws, same questions. One additional question, what does a rooster stand on when he mounts a hen, spurs or claws?
There are big differences in cockerel and roosters. Cockerels often are extremely enthusiastic and many don't have great technique. A lot of the time the females, hens or pullets, don't cooperate either, so a cockerel is more apt to use force. A lot of the complaints on this forum concern cockerels that haven't grown much more than nubs for spurs, yet pullets or hens are barebacked and sometimes even injured. It doesn't do much good to talk about trimming spurs in this situation, the spurs are not causing the problem.
Roosters are a different story. They can grow long sharp spurs. These spurs can be a dangerous weapon. Some mature roosters never develop good technique. Some mature roosters don't have the personality to win the admiration and cooperation of the hens, they still have to use force to mate. With many flocks a mature rooster does not cause a problem with his spurs, but it certainly can happen. I'd suggest that most of the time the claws are what is causing the feather loss and sometimes the cuts, but with the feathers thinned out or gone, the spurs are much more likely to cut the hen.
Another time you may need to trim spurs, usually on older chickens, is when the spurs get so long they curl up and start to penetrate into the legs. Sometimes they get so long it makes it hard for the bird to walk. There have been a few posts with photos on this forum where this happens to old hens, not just roosters.
I hardly ever trim spurs or claws. When I do I use a Dremel tool with one of those discs used to cut metal. I wrap the chicken in a towel around the wings which keeps it pretty calm.
In some chickens the quick grows out pretty close to the end, in others not nearly so much. With some I can see the quick but usually not. I don't try to take a lot off, maybe 1/3 to 1/4 of the spur or claw. I'm interested in blunting the sharpness of the spur or claw not removing it. I occasionally draw a little blood but usually not. When I do it's just a drop or so. I don't know, maybe the spinning disc gets hot enough to cauterize the wound. You can keep stuff like corn starch or flour handy to stop bleeding if you wish, I don't. I just turn the chicken back with the flock, no treatment or anything. Another forum member uses a Dremel tool but instead of a cutting disc she uses a grinder. When she sees a drop of blood, she stops. There are plenty of other ways to blunt them.