That is an interesting question. I got caught up in part of that when the State of Texas was comparing VINs to insurance policies. Somehow, the VIN that Texas had for one of my vehicles had two switched digits - obviously a typo at some point. It was caught not through a traffic stop but when the big computer in the sky received and compared the inputs from the insurance companies. I'm guessing that the VIN is more stable than a license number for that type of comparison.
I've heard stories that some dealers refuse to apply for a permanent plate while a person owes money on a car that they have purchased. They just keep re-issuing paper ones. I have no evidence to suggest that is true. But isn't part of the underlying problem the length of time that it takes DPS to turn around plates? Two years ago, I ended up buy two different cars of the same model one day apart (long story). I sold the first car one day after I bought it and it took 60 days for me to get its tags. It was 45 days before I got the tags for the 2nd one and I ended up getting into a bruhaha with the North Texas Toll Authority over my not updating my account with them with the proper tag numbers. I had remembered that I needed to do that when I bought the car. 45 days later, the idea of doing it had slipped my mind.