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.

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