As others have said working for the government requires a fairly extensive background check. I have had at least two. They even came and interviewed my husband which was pretty funny. Took months. I have a passport, Global Entry, etc. Adding a vaccine part to it is fine with me if it allows me to travel outside the US. Or even to use some inside the US facilities.

Privacy? Give me a break. If you use a computer, you have no privacy. Family DNA will track you down.