Are you going to give someone a checkbook without checking their credit? A checkbook was ye old credit card, and a checking account was how you got it.
I don’t know what to tell you. At least one of my grandmothers needed their husband’s signature to open a bank account in the 60’s, and it wasn’t because she didn’t have assets in her name.
The opposite is also possible: those bought with loans are probably bought new, and would be expected to be held onto for longer. Older cars are cheaper and are probably bought more with cash. They probably also kick the bucket / are re-sold more quickly.