I'd agree in principle with your idea about proof of citizenship, but unfortunately the reality I experienced is I had a valid California driver's license with a Texas address because I had been in the military and California allowed that, but Texas changed their laws to require a Texas ID to vote, and subsequently they also closed 90% of the offices you have to go to to get an ID. Luckily, I knew about this way in advance, but it took 9 months to get an appointment, and when I got there, it required something like four different forms of proof. There were people in there who still lived with their parents who didn't have their own names on any bills bringing their parents in with them to vouch that they actually lived there, getting turned away and told to go fuck themselves. It was extremely transparent and obvious what the state was trying to do, not wanting young people and recent transplants to vote.