I'm not sure that would be so hard to solve. You can record the ciphertext plate and give that to the police.

Really the question is, "How important is this problem? Do we care about license plate privacy?"

A license plate is already essentially encrypted. It's a random sequence of letters and numbers that correspond with a unique individual's information. It contains no personal information in itself.

Except that your car shows everyone the same license plate every time they look at it. This would be completely unacceptable for a cryptographic solution, which would use fresh randomness to respond to every request (in theory).