Why do family RP's even exist?
Because roleplaying always been a popular activity. You could say that family roleplaying is a more childish version of LARP.
I have vague memories of irl roleplaying with my brothers when I was younger. We called it "mom, dad, children" (directly translated from Swedish). I can't recall what we actually did but it sure was popular. Actually, I don't even know what you do on these servers either. So I guess it's quite related.