It's not just that someone else will know that you have chlamydia, it's that they have your data and you don't know what they will do with it. We don't know what they can do and there could be more serious stuff.
Sell it. Health insurance companies are always interested in more details about your health so they can adjust your premium accordingly. Or use it for excuses to deny coverage.
Is there any good reason not to both legally protect privacy and ban the largest part of the market for the invasively collected data (which seems to me to fall nearly under regulating what can be done with the data)?
Only a minority of the world population has universal healthcare. There is a big world outside of Europe and the US and most of it lacks healthcare. Maybe we should focus on the first order problem (for this thread) rather than trying to bring universal healthcare to the entire world (impossible in our lifetime).
We don't have universal life insurance in Europe though, maybe think things through a bit. Your arguments are so thin and bad faith that I'm convinced you're just trolling now.