Or even worse, premiums went up because you could have inherited costly diseases (but didn't), and they have no way to verify it unless you also prostrate yourself on the altar of no privacy.
How confident are you that the government of the country you live in will use the ability to genetically trace the entire population through long range genetic scanning to harm only people you think deserve to be harmed? Keeping in mind that as long as these databases are allowed to exist, the genetic information itself remains relevant for hundreds of years?
Basically, this let's the government put a tracker on every person as long as they can get to where that person was within a couple of months to years (depending on conditions), and every future government gets to decide exactly who should be subject to that level of surveillance, what crime is bad enough to justify it. Do you trust the government of the United States 100 years from now to be that aligned with your personal views? Zero concern that a Hitler-figure could arise in the US and use that power to exterminate large numbers of people?
But I would feel bad if, e.g., insurance premiums were to go up because I had inherited risk factors for some costly diseases.