No, in general the city or state cannot be held liable if you hit a boulder that has fallen into the roadway.

If an obstruction has fallen into the road it is normally up to you as a driver to avoid the object in the roadway and not damage your vehicle. If your vehicle is damaged then you would need collision coverage if you ran into the boulder and comprehensive if the boulder fell onto your car.

You can check with your state's Department of Transportation or like agency though to see what your specific state's laws are regarding fallen boulders. Normally for a state, city or municipality to pay for damages to a car it would need to show that the jurisdiction knew of a problem and was negligent in not repairing it. So if they knew of loose rocks and did not work to secure them or alert drivers to the chance of loose boulders coming down on them then your state may allow claims to be made.

For example in New Jersey, if you have an accident on a state road, you may call the main New Jersey government information line and ask for the state Department of Treasury Claims Service Section to see if your claim would be taken in by them. In NJ, and most other states, motorists are required to prove that their cars were damaged by potholes or other known obstructions. You would also have to show that a government agency knew about the problem and failed to make timely repairs.

In many cases if a claim will be taken in by a government agency you will have a limited time period to make a claim, usually between 30 and 90 days. Attorneys suggest having photographs and a police report. You also will have to prove that a government agency knew about the issue that caused your damage and did not do anything about it in a reasonable time.

You are correct that without physical damage coverages and thus only having liability coverages your vehicle is not covered by your own insurance policy for this type of accident with a boulder. You can contact your state's DOT to see if they would take in a claim for your situation, likely they will not.