No, not all roosters are this way. I would suggest, though, that if your daughter wants chickens as pets, you avoid getting another rooster. In my opinion, a good rooster avoids all contact with me. He moves away when I come near. My last rooster would herd the hens away from me, too. I think your daughter will have a better chance of keeping her hens as pets without a rooster for that very reason. They will depend more upon her than him. Kids are resilient - if you can tell her in a very matter-of-fact manner that Rocky has to go, she'll deal with it much better than if you act like it's a tragedy. It is, in fact, a part of chicken keeping. Sometimes you have to "manage your flock".
You might ask her to think about this rooster attacking her friends or a smaller child.