If I can have a test that is not connected to my persona, from their perspective the data would be as valuable as running a test on the hair in the barbershop or picking a random leftover of food and running test on the saliva left on the half consumed food.
If you're worried about getting arrested for one of the many crimes you've committed, and you want to meet far-flung relatives, you're kind of in a bind here. Assuming unlimited cooperation between the police and the DNA/ancestry services -- which your threat model in this case would require -- even if they don't have your name or address, they could fabricate a half-sibling/double-cousin in the system and have them reach out to you. What, are you not going to talk to and eventually meet the cop pretending to be your previously unknown half-sibling/double-cousin?
Until there's actual punishment for being breached, there will never be data protections in the United States. Even HIPAA and the DMV sell access to businesses.
The only solution to this is regulation and enough incentive that companies have to treat data as they treat radioactive waste material. Storing data should be a liability, not an asset.