All carriers require an ID to obtain a prepaid. The system will not allow the person to put anything in... well unless they were bribed to do that so the number would be untraceable. The result would be a legal address to the someone that actually didn't live there. Other then that carriers like AT&T & Verizon Wireless require the person's information before they can activate the account.
One problem with this law. The phone numbers will be outdated even the IMEI number. Customers can switch numbers and phones faster then a cop can trace them. Especially GSM phones, since the IMEI (traced ID number) can be switched to a new phone just be switching the SIM card.
Or just activate another SIM card. It's that easy ($10) for a SIM card. All it takes is someone greedy at the cell phone store to accept the changes without letting anyone else know.