It's not even gouvernement, it's other companies. One day some insurance company will decide to pull out your protections because, turns out, you have X% chances to get a cancer by your 40. Then all other insurance companies do the same. Then, one of them accepts you, but you gotta pay N% more for the same coverage
You're absolutely right, I can't think of a single point in history where there was mass persecution of any particular group by a government which might have been far more efficient of they had a handy database of every citizens DNA. Just never happens, not once in all of history. There's definitely no shining example less than a century ago.
What if the government in the nearby future decides it is illegal to watch porn? They trace your ip to your house, come with a search warrant, find you cumsock or vibrator covered in dna and you're in the system. Boink! Off to horny jail with you!
One day some insurance company will decide to pull out your protections because, turns out, you have X% chances to get a cancer by your 40. Then all other insurance companies do the same. Then, one of them accepts you, but you gotta pay N% more for the same coverage
The US alone has a rich history of repression (Wikipedia even has a sub-subcategory specifically for ethnic cleansing) and it's common knowledge those DNA databases have been used by US police to track people down so it's really not difficult to link those two concepts. These are concrete examples of things the US government does or has done, not some hypothetical scenario.
And that's all assuming the data is only accessible to governments that have to pretend to care about their citizens, not the for-profit companies and malicious actors that currently do have access to that data.
Capitalism won't let anything about you be yours if it can be avoided and the government works for the corporations. With enough money and government interference anything is possible and it is utterly naive to think otherwise.