Yes, but most of them are not viable in the late stages of a flight. Planes aren't carrying enough fuel to cross an ocean for a second time; most don't even have the capacity.

Please suggest an appropriate international alternate for a plane just about to land in Denver with an hour of fuel remaining.

Alternate airports are picked based with regards to all kinds of contingencies (many of them meteorological), but "the US closes literally every airport" is not one of them.

That likely falls within the case-by-case basis the FAA mentioned, and would likely be allowed to land at a U.S. airport that has capacity.

I'm not aware of a requirement that you need to always be able to divert to a different country.