What do insurance companies do if they have to track down the driver?

That depends greatly on the jurisdiction. Many are badly under-resourced. But not all.

My closest such tale was a few years ago I left a black rental SUV in the parking lot of my hotel overnight. When I pulled in rather late at night the adjacent vehicle was a company-owned white pickup truck with lockers on the back, logo on the door and yellow lights on the roof. Some sort of construction outfit. I wasn’t paying any great attention, but I noted that much.

Came out the next morning maybe an hour after dawn and that side rear quarter of my rental had been trashed by something that was tall and white. The adjacent space was empty. No note of course.

I had to dash for the airport, and of course the rental turn-in took an extra 45 minutes because of the damage. So I never had an opportunity to ask the hotel for any security footage. Both our vehicles were parked in an area and orientation that if the hotel had much in the way of cameras, the whole event & enough identifying information on the truck would likely have been seen.

Gaah!, what a PITA. My credit card’s rental insurance covered all the damage, but that claim process was deliberately designed to be so onerous as to make most mere mortals abandon it half-completed. So I ended up fronting the (grossly overpriced) repair money to the car rental company (one of the biggies) for about 6 months before the CC’s third party “cardholder benefit provider” finally coughed up the dough.