You have to show ID to get voter registration in IL, regardless if you do it ahead of time or at the polls, it's just that the ID is not federal. The same situation (no federal ID needed, just proof of a portion of identity) is found with this and I really don't see either of those being measurably better/worse with a national ID.

Not that I would mind a national ID. It's a real annoyance moving between states & I'd love to say "sorry state xyz, I'm already registered nationally and don't need a regional ID" when I move.