Of course, all the testing agencies are collecting DNA. The records will be somewhere.
Do we think that government agencies will be able to access these? Will the NHS? Will government access even be stated in the agreements that they signed to be 'government-approved'? Will the data be available to other companies down the line for research? Or when they are bought up by a big corporation?
The point is that this is another erosion of privacy, another cat is out of the bag. It is all very foreseeable.
Once we sanction the collection of private information, eg DNA for health! to prevent child abuse! to stop terrorism! the over-reach is never withdrawn. Government access to your dna, online record, etc, etc - becomes the new normal. All while the actions of the government are ever more hidden - eg secret courts, collection of data, etc
In every instance of privacy erosion, a plausibly valid excuse is supplied by the government. But it is a one-way street. Why we continuously accept government justifications of excessive over-reach amazes me. But that we do in general (I don't!) destroys privacy for everyone.