While it may be an important part of the police job, it is not treated as such. It seems everything takes priority over the impound yard. When you have been standing in the impound for an hour requesting service and you are watching police drive past you (without their lights on) it gets really frustrating. Also, when it does happen, there isn't any fantastic RP to write home about. The police and the person getting their car generally don't want to be there and are trying to get through the process as fast as they can to go and do other things.
Maybe meet in the middle. Have a timer start (15 minutes) and if that timer ends before someone comes, then it becomes automated. It would be interesting to see how many manual services are done vs automated in this scenario.