The person I used to stay with when I used to visit WV don't have a proof of citizenship. He doesn't know where his birth certificate is (probably with the US army if they kept track of their nurses giving birth on ex-allied territory during a war), and get by with is SSN and driver license.

How it works in my country : my electoral card is freely sent to my address when I register to my voting office. I can vote with it, or with an official ID, as long as I'm in the correct place. The only moment I need my ID is to cast a vote on behalf of someone who identified me as a 'surrogate'.