The point is that people who are obsessed with vengeance or greed do stupid things that lead them to their deaths. As Vito said in the novel, "Revenge is a dish best eaten cold."
Exactly!
Carlo had just suffered a lengthy and intensely humiliating public beating at the hands of his brother-in-law. He wanted revenge and he wasn't thinking beyond that.
It is a bit of a stretch to think he would hang around afterwards but then again he probably hadn't thought things through that far. Maybe he thought being married to Connie would give him a pass if things came to a head...