I generally agree. No sympathy for that sort of behavior.
That said, the police has recorded the accident, so there is already punitive effect with respect to his driving record.
Secondly, he will incur a financial cost, whether that is through increased premiums (as a result of a claim PAID out), OR as a private settlement.
So the guy will have been dinged on 2 fronts, regardless. With the latter case, the OP might derive a bit more psychological "satisfaction". (Not to mention allaying his professed (1) anxiety over disassembly of vehicle (2) wastefulness of claim (3) satisfaction with the cosmetics of the car).
This is about seeking the optimal net outcome for all parties. Not about vengeance or extortion or illegal or amoral activities. As my final post on this thread I hope that intent has been made clear.
This is where I lose you. "optimal outcome" is not a consideration for someone who ran from an accident... full stop. The "running" party lost any consideration for an optimal outcome for him. Also like I said, the person running has already proven that they didnt want to accept responsibility for this.
Lets spin your idea forward... Say OP followed your advice, and contacted this person directly and tried to negotiate some sort of direct settlement. What about the person who performed hit and run says that they are actually going to follow through on whatever they agree to? What then? Call the cops and say "I made a side agreement with them and they didnt pay? (no)". Show up at their house? (no).
Making a personal agreement in such a case requires some trust, as you would have to trust that the person would "perform" on their end of the agreement.... and what about a person who tries to perform a hit and run says they are responsible and going to perform on their agreements?
As I said, the proof of how "they handle business" is already right there... they ran. Sure we only know about "that one time" but thats all thats needed if OP was even thinking about cutting some sort of side deal. Its a silly idea in this case because that person ran... and I dont see any argument that makes any sense at all for a personal contact with them on a side settlement.