In Canada all elections have this option, and no one complains. Just show up in the correct voting station, show two pieces of government ID with your name, address and picture on it, and you're allowed in.
Oh, but the people who favor same-day voter registration ALSO oppose voter ID! Think about that.
That's actually the law in Minnesota. You don't need ID to vote if you're already registered, you just have to say your name and they check if it's on the roster and that person hasn't voted, if so, you sign next to the roster. You don't even need ID to register, you just need for someone already registered to say that you live in the precinct. And if you register without that, you do need some proof of address, but no photo ID.
Do you realize how open to fraud that system is? All you need is for someone to say that you live there, and they will let you register and vote?