It's overblown. It's mostly propaganda.
I just have to show up with my ID
My ID is good for 5 years, and I am required to update it within 60 days of changing residences. Every time I've renewed or updated it, they have asked me if I wanted to register or update my voter registration. My registration is updated every time I vote, and I don't get de-registered unless I skip voting for about a decade straight, without re-registering when I renew my ID card.
ALL of the problems with voter registration are about people who either can't or won't get or renew their ID card. Every time you read about voter registration issues in the US, you should imagine going to your polling station without a current ID card.
What I'm describing has been federal law for over 30 years. The European criticism about ID cards is nonsensical. Every time you obtain, renew, or amend your drivers license or ID, you update your voter registration.
Remember the context of my comment: I am replying to European criticism of registration. The European approach is for everyone to obtain a government issued ID card and present it at the polling station. The NVRA already does this. We have already adopted the European solution to this problem.