Car through a fence- question

Last Friday my 19 yr old son was eating while driving, got distracted by a food spill and went off the road. He took out a fence post but the barbed wire survived. No other vehicles involved and he was uninjured. The car was damaged and so was the fence.

My question is, should I report this to insurance? The vehicle had liability coverage only so he’s on the hook for vehicle repairs anyway. I see no reason to report the accident and possibly raise insurance rates even though no claim is filed… but…

1) the fence is owned by the highway department (Wyoming, US) so they could send a bill for fence repair, and

2) my son got a ticket for improper lane use, which he paid. The highway department will know who to send the repair bill to. If he gets a bill for fence repair, and we then file a claim against the liability insurance, will we be in trouble for not reporting the accident in the first place?

I want to do things correctly but don’t want to further complicate the issues at hand.

TIA.