[Disclaimer: my predictions of the behaviour of insurance companies are based on my experience with North American ones. I have no reason to believe European ones are different.]
The word pothole has two meanings. The first is a small area of road a few inches lower than the rest, with sharp edges:
This really shouldn't damage your car. If it does, any insurance company could probably say it was your fault for not driving in accordance with the road conditions. With proper driving, a steady diet of this kind of road might require a "front end alignment" more frequently than usual. It is not worth your time to try to get someone else to compensate you for that. If you break an axle or something else dramatic, it will probably be as a result of improper driving.
The second meaning of pothole is a huge round hole that can swallow entire cars:
This picture might be fake, but it depicts something that does happen
Should you meet one of these, I suspect your insurance company will go after whoever designed, built, and maintained the road, seeking compensation for your damages. They'll pay you and save you the trouble of pursuing the relevant local government yourself. That's one of the purposes of insurance.