More Waiting

Where does the logic for this scenario come from? My office receives a phone call from one of our Client's mum who says her son has attended at the Police Station for an interview by appointment. We receive the phone call half an hour after the appointment time. I run off the Police Station where the Client (who is an adult) is waiting. We then go through to the Custody Suite where it takes just under an hour to book him in, take his samples etc. The Police knew that it would take me about 30 minutes to get to the Police Station, and they are well aware of the time that it takes to process a Client until he can be seen by a solicitor in consultation, so why did they not book in my Client whilst I traveled to the Police Station? Would it not have been more logical to go through the arduous process of booking him in whilst I was en route to save their time and my time?