Look at Spain. We have been using our IDs for decades and it’s a great way to solve that problem. You just go to the voting table, show your ID (DNI) and vote. That’s it. And it works for everything related to anything official.
But because of the voting system we don’t have gerrymandering (or at least not that much).
In the US case it should be a federal ID. With a 6 or 7 letters ID should be more than enough. And compulsory at 13 y.o. You can drive, you have an ID.