This is not how it works now.
Even without photo ID, a voter must confirm that they are registered before they are permitted to vote. At my precinct this consists of giving my full name and address, which the poll worker confirms against a list they have of currently registered voters.
If you wanted to steal my vote, you would need to know in which precinct I'm registered, then you would have to go there and give them my full name and address. Not impossible but not "anyone can walk in and vote" either.
Requiring photo ID only makes sense to people who don't understand how the voting system works now. It's very hard to mess up more than a few votes in person. It would be impossible to steal an election that way. And numerous studies of actual elections have shown that to be true.
Meanwhile, the requirement for photo ID reliably messes up the vote for hundreds of thousands of people, mostly poor and minority. Which is the whole point, of course.