A rooster's 'duties' are two: to protect the flock from predators (by sacrificing himself if necessary)
You put a lot more faith in a rooster being willing to sacrifice himself than I do. A good rooster tends to be a good look-out and early warning system, especially for flying predators. If a threat is identified, a rooster will usually put himself between the flock and that potential threat and check it out. That makes him more vulnerable, maybe that is what you mean. Once a threat is identified my roosters are more about leading the flock to safety than fighting a rear guard action to give them time to get away.
There are always exceptions. Sometimes a rooster will attack a threat. I've seen a rooster run crows off that were eating treats I'd tossed in the run. I certainly believe the stories on here where a rooster attacks a hawk, cat, or other critter that is a threat, perceived or real. I'm convinced that can happen. But my experience is that when a large snake is eating eggs the rooster does not attack, but the entire flock is giving an alert call. In the two dog attacks that cost me 13 chickens the dominant rooster did not lose a tail feather.
and from one another (bullying), and make more chickens. That's it.
To me part of a good rooster's duties include keeping peace in his flock. I think with chickens the term bully gets used too much or can mean different things to different people. Do you consider sorting the pecking order among the hens to be bullying or chickens being chickens? Sometimes a dominant rooster will break those up, some don't. I've seen a rooster help a broody hen take care of her chicks, especially when she gets separated from some of them.
I raise juveniles with the flock in an outside area over 3,000 square feet. It can get pretty rowdy between the cockerels or between the cockerels and the pullets. My dominant roosters usually leave them alone as long as it is between the juveniles. If that spills over to where his hens are being bothered he gets involved.
Some roosters help hens and pullets find a good nest. When they hear the egg song some of my roosters leave the flock to go to the hen and lead her back to the flock. A rooster should find food for his flock and call them over to eat and let them eat first. He doesn't get involved in the keep-away games if they find a nice treat but lets them have it. He may see that they are all in the coop at night before he shuts it down.
A lot of these actions depend on the size of the flock and how we manage them. The smaller the hen to rooster ratio and the more room you have the more likely you are to see some of these. Not all roosters do many of these things. I'm only talking about mature roosters that are flock masters, immature cockerels are totally different animals. In most of our flocks you won't see many of these behaviors, conditions aren't right. But a rooster has a lot more duties in a flock than just to protect against predators, stop bullying, and fertilizing eggs.
In my opinion the only reason you need a rooster is if you want fertilized eggs. In a flock without a dominant rooster the dominant hen will assume some of these duties. Those all-hen flocks can get along very well. Other than for fertilization I don't think you need a rooster for a peaceful tranquil flock.
Chicken society can be fairly complex but if every member does their part it can function very smoothly. A dominant hen that won't allow a rooster to fertilize eggs or lead the flock can disrupt the peace and tranquility of the flock. It takes all of them working together.