How does knowing make anything different?
I'd want to know for serveral reasons. Maybe there's another side to the story and he/she has video showing that I made a mistake causing the wreck. The reality of situations can easily be skewed by ones own perspective. Or maybe the driver is just a jerk and you want to know to be especially cautious around them the next time. There are also other good reasons.

At some point I do agree it's gotta be chaulked up to just one of those things and put it behind you. Then again, that is a heafty bill!!