Bullying other roosters is the #1 job description for becoming a rooster.
If all roosters are more or less equal in age, size, physical ability, and libido then they may coexist.
Roosters do not become more aggressive as they age, they become more mature.
Maturity in male animals usually results in the male in question becoming dominant, and dominance usually results in that animal assembling a harem or else bossing a large territory in order to mate with as many females as is possible.
The only way that a rooster can accomplish this feat is to suppress his competition. To a large extent roosters crow to accomplish this but they also must back up their verbal threats with displays and physical daring do.
With enough ground to roam and a sufficient number of hens I have seen real rooting tooting gamecocks free range together but each rooster had his own distinct area or walk to boss. Also each walk had its own physical features to rally around, like a old house place, the new home place, the hog pen, a mule stable, an apiary, the cow shed, the orchard, and the dog pen to call home and each walk or run also had its own water and feed resources and acceptable roosting areas. Because there were no fences or pens of any kind, the hens did trade from walk to walk and often a rooster would try to herd a wayward hen back to the roosters' home area but if he reached the boundary of his Kingdom he usually pulled up. I am unsure if the rooster was loath to leave his harem behind in order to pursue one unfaithful hen, but that is what it looked like. Maybe the roosters realized that 100 or more hens in the hand was worth more than one fickle hen escaping to his neighbor's walk.
This farm covered over 500 acres and the features were scattered over about 40-50 acres of it.
In my long years with chickens I have never seen a real dominant rooster be violent, at least as chickens score violence with a hen. In my considerable experience hens look for the rooster and voluntary submit to him. They do this by squatting in his presence and remaining squatted until the courting ritual is finished and mating is accomplished. All the squawking and flying feathers is because the hen is adverse to being mated by (to her) an inferior or low ranking rooster.
Roosters are jealous and one problem you may face is the dominant rooster pulling or knocking his competition off the hens' back every time the non-dominant rooster tries to mate. This is one way that you can end up with infertile eggs even though you have sufficient roosters. The dominant bird is too busy policing his run to mate and the non dominant roosters never completes the act. Too many roosters like too many cooks spoil the soup. Commercial hatching egg operations don't experience this problem because despite all the new chicken keepers opinions about the innate aggression of commercial hatchery birds, the opposite is in fact the truth.
That said I have seen non-game roosters form partnerships with a near dominant bird and with the dominant rooster standing aside to allow the runner up rooster to tread a hen once the dominant bird had finished. I think that this is not a conscious strategy but that it represents a slow change or transfer of dominance.