Should cars have "sorry" indicators?

On my way to work this morning, I witnessed a guy cut someone off unintentionally. I could see his body language because I was temporarily next to him. He was saying, “sorry” and waving in a meek way. The guy behind him was having a tantrum, and it looked as though he was going to rip his own steering wheel off and throw it at him.

Cars have turn signals, break lights, and hazard lights. What if we had some uniform set of additional signals that were to identify intent to our fellow drivers? What if you could throw a “sorry” signal? Do you think this would help calm people who feel they have been done wrong on the road? In “real life” (non-driving), a simple, “Sorry, I did not intend to…” can go a long way.