On the US keep in mind elections are run at the state level and below, so we don't have a single voting system, we have 50+.

My state, Oregon, for example uses a very straightforward vote by mail system. They ask if you wanna register to vote when you get/update your drivers license or state id. Your ballot just comes in the mail, you fill it out, send it back. For folks that lack a permanent address or similar, you can get provisional ballots at libraries and similar city offices. The provisional ballots make you fill out enough information to check if you're allowed to vote.

It's simple, convenient, secure, and efficient.

So why don't more states do it this way?

Unfortunately there's a long ugly history of using all sorts of dirty tricks for voter suppression in the US, in particular to keep Jim Crow going. And unfortunately variations of that continue today. I don't have the energy to dig into it fully here, I just want any international readers to be aware there's a whole lot of utterly craven bad faith when it comes to discussions around voting fraud and security in the US.