That system would also allow us to completely get rid of our horrendous voter registration system, and make universal voting a reality.

The failures of the US voter registration system are deliberate, targeted disenfranchisement.

It would. In fact, Sweden has no “voter registration” per se, everyone who is registered as living here just gets a voting card in the mail before the election, I did earlier this year. (I only moved to Sweden this year and had no idea how to register to vote, turns out I don't need to!)

It's not great for privacy though, so I understand the resistance of the US and the UK to it. Mind you, the US wouldn't have to make the whole thing public like Sweden does for… reasons.

What if you have like 10 addresses? Can you vote 10x?

One registered main address per person, though you can register an additional “special post address” if you want to get your mail somewhere other than where you sleep for an extended period of time. You can't vote twice even if you did get two cards, you have to show ID (which I dislike, but it's at least relatively easy to obtain here) and your name is crossed out on the voter list once you've voted.

Lots of countries use the tax system to automatically sign up voters. Obviously this doesn't catch all potential voters - the people who don't file taxes because they have no income are likely a lot of the most disenfranchised individuals - but it gets you 90% of the way there. In Canada, whenever you file your taxes you have a box to tick 'automatically share my information with federal and provincial elections authorities'.

While it's administered by the Swedish Tax Agency, what Sweden has is actually a general population registration system that everyone* has to be in and which is used across the entire government.

*Asylum seekers and various types of temporary residents and such are not technically considered to be in the population register, though they are usually still in fact in the database, just with less information and a flag saying they don't count

Except in the USA, voting is constitutionally a state thing, not federal.

Federal laws, oversight. Local administration.

https://www.eac.gov

Cue the fever dreams whenever anyone merely suggests we harmonize, normalize the details. As if predictable standards for signature verification will inevitably lead to a military coup.

Even if that were entirely true, which it isn't, the Constitution is not fixed (except maybe the part about equal representation in the Senate, and there's a two-step trick to change that, too.)