The 10 to 1 ratio is about fertility only. It is not a magic number concerning roosters fighting or barebacked hens. Some roosters are more vigorous than others. Most full sized roosters can keep many more than 10 hens fertile, but some are not energetic enough. But if you have a flock with one rooster for every ten hens in that flock, you can be pretty sure that all are fertile.
The 10 to 1 ratio has absolutely nothing to do with whether roosters will fight or how vicious those fights will be. When you have more than one rooster in a flock, one will be dominant over all the others, whether it is one other rooster or six other roosters, whether there is one hen in the flock or fifty. They determine which is dominant by fighting. They do the same thing to determine the pecking order. The dominance fights are often more vicious, but the pecking order fights can also cause chickens to die. Usually one rooster will dominate the other and they become a good team, working together to take care of the girls. Sometimes neither rooster is willing to accept the subservient position. In this case they fight to the death. Old English Game Roosters have a reputation for this, but it can happen in any breed. And sometimes the dominate rooster will kill a much weaker rooster that might be willing to accept the subservient position, as if to say the weak one does not deserve to be his partner. He can't trust the weak one to defend the flock. So their personality has a whole lot to do with it.
There are other factors involved too. It does help if they have a lot of room. That way, the roosters are not in each others face all the time. I had about 15 hens and three roosters while I was deciding which rooster to keep. The dominate rooster and one other rooster hung in a group with about half the hens. The other rooster and the other hens hung in a different group. They slept in the same coop at night and I could leave them locked in the coop and 12 x 32 run without them fighting, but as soon as I let them out, they separated into their groups. I think having separate food and water spots helps keep conflict down too, but I only had the one.
If roosters are raised together in the same flock, either as brothers or in a father-son relationship, they often work out their differences at a very young age. You may not see a lot of dominance fighting, even when they are young. At any time one of the others may challenge the dominant rooster and a vicious fight can ensue, especially when a son gets mature enough to really challenge his father, but even then these fights often do not end in serious injury.
Any time two roosters meet each other for the first time, they will fight for dominance if hens are present. If you separate roosters for a while then put them back together with hens present, they will fight for dominance. These are the fights I most worry about serious injury. It is still quite possible that one will accept the subservient position and they will get along, but as I said, these are the ones I worry about. So if you do keep more than one rooster with a flock and they get along, don't go swapping them out or adding more roosters.
The 10 to 1 ratio is certainly not a magic number concerning barebacked hens. There are a lot of factors involved with whether a hen is barebacked or not. Some of it involves the technique of the rooster, the difference in size between the hen and rooster, whether or not a hen resists, how determined the rooster is (usually worse with an adolescent), how much room the hen has to get away if she does resist, and other factors. How many hens are in the flock does make a difference, but one poster on here had one rooster and 18 hens. Some of them were barebacked. Not all but a few. I think one way to help dispel the myth of the 10 to 1 ratio being a magic number concerning barebacked hens is to read this thread. I have a lot of respect for the experience of a lot of the posters in this thread.
Breeders managing roosters
https://www.backyardchickens.com/forum/viewtopic.php?id=250327
My normal recommendation is to keep as few roosters as you can and still reach your goals. The more roosters you have, the more likely you are to have a problem. There is no guarantee that having more than one rooster with a flock will cause them to fight to the death nor does it guarantee barebacked hens, but both are possibilities.
Good luck!