This is not true. For example not every citizen can vote (people under guardianship or criminals) and not citizens can vote in local elections in the EU, if they came from another EU country.

Yes, but a driver's license can be accepted as ID.

Just because a driver's license isn't proof of citizenship doesn't mean that it isn't sufficient, since it will have some identifier connected to the identity of the voter. You would show the driver's license, then the registrars would find your name on the list, strike it out, give your voting envelopes, and then you go wait for a private booth to become free and then you go into that booth and put your votes in those voting envelopes.

A Swedish driver's license doesn't mean Swedish citizenship. It can still be used to check somebody's identity. Citizenship is checked by seeing whether the person is on the voter rolls, not by their identity card.

> In Europe, you can't get a regular ID without being a citizen. So having an ID automatically means you're eligible to vote.

Nitpick: E.g. Norwegian ID cards can be had by any legal resident. The card will say that you're not a citizen though, so your point about that stands.

Re driving license: Driving license is a valid form of ID for voting here. All eligible people are on the voting rolls automatically (unlike the absurd american system), and the driving license is merely used to prove you are who you say you are.

In my state government issued ID is used to verify who you are. You are then issued a ballot if your name is also in the poll book.

Your eligibility to vote and have your name entered into the poll book is determined by providing a Social Security number or birth certificate.

So yes, a driver’s license is sufficient ID to vote in many states.