Here are a couple of scenarios:
1. A person permanently moves from California to Arizona. Does your system invalidate that person’s voter registration in California?
2. A person resides part-time in two states. They are registered to vote in State #1, but have their absentee ballot from State #1 sent to their address in State #2. Does your system prevent people from voting in two or more different states?
With driver’s licenses , when you move you have to surrender your old license to get a new one. Same system could work here.