What’s to stop you from voting multiple times? Or voting as someone else? Or someone else voting as you? That last one actually happened to me during a presidential election in my home state.
I don’t think it was part of some deep state plot to steal my vote, I’m betting some distracted volunteer at the polling place accidentally crossed off the wrong name and handed someone else my ballot. But still, it seems to me that if we can give out free IDs (which is a thing in my state) then there’s no downside in checking them during voting in person.