As a keeper of a flock with multiple roosters, I concur with most of what is written here.
Where I depart is on defence of the flock. Most roosters will face down a moderate threat, like a regular domestic dog or cat come onto their territory and standing looking at them; but they'll bolt if it's running aggressively toward them. Some roosters that get caught may fight a predator to the death. But more often, in my experience, when a life-threatening predator appears, they sound the alarm to scatter, and then run into hiding as fast as they can, along with the rest of the flock.
Roosters are essential to the physical and mental health and wellbeing of the flock, in my view.
