No, they don't.
In fact, just wait until the COVID-19 vaccine passport becomes a general-purpose medical passport - unless you have all the right shots and none of the wrong diseases (politically determined, of course; HIV will still get a waiver), you aren't traveling, you aren't working, you won't have a house, and if you're lucky, you might still be able to scrounge some food from the dumpsters in the alleyway.