I don't know, I would find it useful. Every time I have a vaguely suspicious symptom I wonder about it. If I tested negative I would be pleased and resolve to make sure it stayed that way. I think that would be a general response. A positive test would prevent you shilly-shallying about if your symptoms worsened beyond manageable.
There will always be idiots, but I'm not in the mood to protect/pander to them. That's my "off the top of my head" view - I might be very wrong.