@newstik @ricci @q_aurelius @mekkaokereke @MHowell @georgeeyong @oscarjiminy @carnage4life
That's also how it works in the state I live in, they have you sign the roll to verify you voted. If you want to vote from somewhere other than your registered polling place you can but they have you fill out a provisional ballot so it's slightly more hassle. They could definitely make this easier, but you don't have to show ID.
I presume they look into your eligibility when processing your registration, so it's taken care of long before you get to the polls.
I do my voting by mail these days because I'm disabled and at higher risk for Covid and other junk. It's very convenient and should be more easily accessible.