You probably call peacocks peacocks though, even though the "correct" collective name is peafowl.

That might be a regional difference: I've heard cock or cockerel plenty of times in British English. We even sang a song at primary school called "The Golden Cockerel" in assemblies: https://www.youtube.com/watch?v=IkoWrj_IBWo

It has become more common to say rooster in recent times, sure, probably because of the slang usage.

Fun fact: Rooster Rock in Oregon looks nothing like a rooster, because it was originally Cock Rock. Because that's what it looks like, and even the Indians named it for that.