I did hear a story about a group of students who had a non-working car. When term started, they'd call the AA and say the car had broken down and they need to get to Oxford. The truck would take them in the cab, towing the car. At the end of term, they'd call the AA again as say they needed to get home to Sussex (or wherever). Almost certainly apocryphal but a reasonable yarn.
These days they won't recover anything without a valid tax disc displayed.
I know of at least one person their recovery company (might have been AA?) wouldn't help because she didn't have her tax disc to hand - like a lot of bikers, she didn't attach it to the bike. The bike was taxed and fully road legal, but they wouldn't help
I've certainly not displayed a tax disc on any of my bikes for many years. Some of them it's in my wallet, others on the keyring - it's a valuable bit of paper and easily nicked, why make things easier for the scum of the world*. No copper has ever given me grief for it, why should any recovery company?
*I include the DVLA in this heading.