You're absolutely right. I'm not saying any of this is easy, nor am I saying that an antibody test will give 100% accurate results. It will give false negatives and false positives which, depending on the context, can be problematic.
What I am saying is that use of a person's immunological status is maybe in that person's own best interest. Wouldn't you love to know? Wouldn't you love to know if you were immune right now, and you could go out into the world and take it on without fear? I think most people would like to know that, but to get to a point where they can know that, or society at large can know that about groups of people, is going to require putting some water in the wine of personal privacy and how health information has been handled.
There's a knee-jerk way of thinking that any dilution of privacy of health information is terribly bad. It needs a more studied look than that.