You can still get in with a negative test even if no passports are recognized between EU / US. Getting tested maybe annoying for sure, but it's part of the scheme going to Switzerland, and presumably to EU also.

I think everything depends how long the covid is issue to the hospitals of the destination country. If the vaccines are very potent, as it looks like from in Israel, then it might be that most of Europe & US can already travel freely without passports at the end of year.