I assume that we can learn a lot from other places, but I’m not sure that everything that works for one country always scales to a population 5-10x larger.

I see this kind of thinking a lot. I call it "inverse American exceptionalism" - the idea that something tried-and-tested just couldn't work in America for some unknown mystical reason.

Mandatory resident registration (which enables automatic voter registration) is not something that has just been tested in a few small European countries. Aside from many European countries, it exists among other places in China, Iran and Japan. Not that it would be sufficient if it were true that it exists only in small European countries to conclude that it couldn't work in the US.

No, the reason you don't have automatic voter registration, or universal access to health care and education, or a minimum income guarantee, or any of the other basic staples of prosperous societies, has nothing to do with the US being large, or having a constitution, or having a federal structure. You don't have those things because your politicians, largely with support from your voters, deliberately choose not to implement those things.