In a practical sense, how would law enforcement cope with the fact they have no record of who owns what car (even more difficult if no one has license plates)? That's not to say they have a right to know.
Hmm, just a thought though, and this might not fully replace the current system, a private database could be created and people would voluntarily "register" their vehicles. I know I might want to do something like this so my car could be identified easily if it was stolen. So this service could be free to law enforcement or they might have to pay (depends on the owner of the database). Obviously if someone wants to use a car to commit a crime they wouldn't use license plates or "register" their vehicle so there's still that issue.