I experienced that too, but the difference is the owner of the car saw me.
The owner of the car has insurance, the insurance company can pay it if he can't find you, but if you go to the police station yourself, your insurance company will pay some, you have to pay some too, sounds like that you have to pay a lot of money to fix the car if you report it yourself.
Maybe you have to risk of rising up your insurance fee.
I will choose to go away if I were you even though I know the right way is to report it, but I don't want to pay to fix it cause usually It costs a lot of money.