We have issues with voter registration because it’s been politicized. Poor people are disproportionately less likely to have ID cards (because it costs money, takes time, and most people get it to drive which is expensive), less likely to have it up to date. It’s disenfranchising to mandate IDs. Whether or not it’s a problem falls down party lines and your favorite statistician’s analysis. But that’s why it’s “an issue”.
Part of the issue is that you don't need an ID in America for most of your daily life. Most people get it to drive - if you don't have a car (which is actually expensive) then you may not get an ID at all. Yea most people will get an ID, but it's not something people need.
When it comes to the cost of the ID, part of the cost is taking time out of work to sit in a crummy office and fill out paperwork. They require certain proof of identity paperwork that can be hard to get for certain walks of life. Its quite an edge case in society that can't produce a small amount of paperwork to self-identify, of course.
Its a small cohort that truly don't have the resources to get an ID, but there is almost no observed downside to not requiring IDs to vote - American elections are and have been perfectly legitimate (or until 2020, depending on who you ask...). Why would we put up extra barriers to vote when we could just... not?
You need to be on their list though, but you get added automatically by the city to the list. When you move you need to register your new address, so they know that you live there.
