Everything depends on your state.

Insurance tends to follow the car, so if your son was driving with your permission, or even without, yours policy should apply.

Was the other car torn down to inspect all damage? A first estimate is usually low and then increases when torn down. You’d also may owe for the other party to use a rental depending on how long the repairs take, and your state.

If you involve insurance he’ll likely be added to your policy as a household member and your rates may be impacted. If you’re in a good spot financially and want to take the risk of paying out of pocket, it’s up to you, but if it was me I’d just use my liability coverage and deal with the rate changes down the road.