There will be a notice at the entrance to the carwash stating you use it at your own risk and the owners will not be liable for any damage, etc. That does not get them out of their public liability to maintain the thing properly, but the handling agent stated that it was working properly, there were no faults and there were no other problems with any other vehicles that day. What could have happened is that the spring in the wiper arm snapped allowing it to flop free and be gathered up by the rotating brush and torn off by it. This is the most common reason for rear wipers being torn off in carwashes. It has happened to other readers.

So you would only have a case if you could prove that other vehicles had been damaged that day. Maybe a local newspaper or local internet forum, or even a postcard in a newspaper shop window would enable you to find any others. Once you did you could claim for your time as well as the damage, using the letter from the insurance agent to prove that the insurance agent had lied.