This isn't the whole picture. In some states, there's a proof of citizenship requirement in order to register to vote, and the most common form of photo ID (driver's license) is not sufficient for that purpose in most cases, because non-citizens can also hold it.

Problem is, for many people, they don't actually have any documentation to that effect. The most typical documents are passports and birth certificates. The former aren't free, and are otherwise only really useful when travelling in other countries, so there's little incentive to have one. The latter are often not available on hand, and you have to go to a completely different place (from where you register) to obtain yours; worse yet if you were born in a different state. It's usually not free, either.

http://www.demos.org/publication/how-do-proof-citizenship-la...