Having recently dealt with an insurance claim, it seems that the insurance companies do not care about the high cost of coverage. Higher expenses just mean they can justify higher premiums.
I had some very minor damage. Another car rubbed my front bumper when trying to parallel park. The only damage was a small area where the plastic on the bumper was torn. They had no problem paying for a new bumper for a total cost of a bit over $2000. I even qualified for a rental car for the week the repair took but did not need it.