Incorrect.
People keep flocks of entirely roosters all the time, whether it be they're raising them for meat production, or if they're just giving their breeder hens a break. I have a pen specifically for the boys when I don't want them harassing the hens.
ETA: You cannot do this with every...
I've got a bantam Splash split to Chocolate Orpington cockerel. Visually he is Splash, but carries one recessive copy of the Choc gene. He's a bit big for a bantam, so I won't be using him for breeding. He's never been aggressive towards me.
I can take some pics tomorrow, if you're interested.