My country requires ID to vote. You also have to bring in the enumeration document saying where you are allowed to vote that includes name and address.
same here you need 2 documents ID + card issued when you register for voting and you can vote only where you are registered.
Only voting where one is registered is a good way to prevent fraud. There are many cases where busloads of people vote at one place, and then are transported to the next voting place, etc.
Even at the same voting place, some people would wear disguises including hats, mustaches, wigs, etc. I'll bet Hillary brought suitcases filled with every color pantsuit she had, and probably tried dark glasses and a mustache too!