Most countries register their citizens to vote too, and have national ID. If you were already registered to vote in the entire union automatically, and you had an ID-card (like the SSN, but actually good for identification with any security built into it) that would work everywhere in the US I wouldn't have a problem with requiring voters to ID themselves.

Why the US refuses to do either of those things, instead putting a lot of hassle on the population when election participation is so low it jeopardizes the fundamentals of democracy, that people feel like the government actually represents them, I have no idea.