Shouldn't. You're right. But Glaswegian dvla employees are a rare breed
It used to be instant and then you had to wait for the documents to arrive. They change the tax disc there and then....
Recently I heard they done away with this service in there office and it now takes a few days.
Took my mate 2 weeks for his stuff to changeover from his q7 to his 5 series he just bought. That was done through a dealer and included the time for the documents to arrive.
When you transfer a plate on retention onto a vehicle then it's instant. When I bought my private plate I got all the documents sorted at the office and they printed off a new MOT certificate and tax disc with the new plate on, the log book was sent via post though. I was in the DVLA car park changing the plates over - boy I was like an excited little child! They do let you keep your old plates on your car for 2 working days before you have to change it over.
I had to send my old tax disc back to them to prevent fraud, I forgot to send it back though.