You are on a conservative site and you suggest a big brother tactic like that? We already have a "tagging" device on cars, they are called license plates. See, the number on each plate is original to that car, so when a cop gets close enough to get the number, he can then back off, radio in and get the name, address, birth date, hair color, eye color, what type of toothpaste the owner of the car uses and use this info to later go to the home of the traffic violator and arrest them.
In my county the cops use this tactic quite frequently to good affect. They can also radio ahead and have the nail strips placed in strategic spots if the criminal is wanted for something other than running a red light of speeding. There is no need to go any more nanny state than we already are.
What if the plates don't match the car?