The real weirdness in the US vs the rest of the world is not that you have to get a court to issue a divorce or that there isn't a central registry, but rather

The real weirdness in the US vs the rest of the world is not that you have to get a court to issue a divorce or that there isn't a central registry, but rather there are literally fifty separate systems, all with slight variations, and you're not locked into a particular one. Divorces used to easier to obtain in Nevada, so people would go there. Certain states adopted same sex marriage before others, so you'd go there.