WHen I lived in Jersey, we did the same thing, kept the plates.
When I moved to Georgia, nearly 30 years ago, it was a little different. The plates stayed with the vehicle, and I can't tell you how many times buyers would simply not re-register the vehicle, until the tags on the plates, expired.
That's been changed about 15 years ago, or so... Now, the plates belong to you, not the vehicle. It's made things so much better.