That legend of them crowing to greet sunrise is not necessarily true if you are counting on them as an alarm clock, though it is pretty common. One of the purposes of crowing is to tell other roosters “This is my territory”. What better time to do that than first thing in the morning?
Some roosters crow a lot more than others. My current is likely to crow inside the coop before I let them out, but once outside he’s too busy chasing hens to crow for a while. Late morning or early afternoon, and often both, he gets in a crowing contest with a rooster about a half mile away. In the country, those crows can travel a long way.
I hear what sounds like a crowing rooster sometimes when I am outside so I was curious if that rumor was true because I don't think I have ever heard it early in the morning. Or maybe it is just not loud enough to be heard from inside the house.