At a minimum, it is worth pursuing a carrier through the first few levels of argument. Depending on the country, the value you place on your time, and your tolerance for process, it may or may not be worth pursuing on one's own.
On the other hand, the claims agencies do serve the useful purpose of weeding out silly claims. As there is only a fee to be had if the claim is paid, the agency has no incentive to take cases where one is tilting at windmills, either out of anger, spite, or ignorance.