I think it's worth mentioning that while biometrics for identification have flaws (as mentioned in this thread, they're not 100% collision free, are not necessarily secret, and are non-trivial to collect), DNA has a different risk profile if it leaks than fingerprints and iris scans if you consider technology advances. DNA could let people (moving beyond government, since you should probably assume anything in a government database will be leaked at this point) target your family and not just you, it includes information that could let adversaries find out ways you're uniquely exploitable (for instance allergies, sensitivities, diseases) and in general its potential for harm goes far beyond impersonation or being used in court.

(On the plus side, I suppose, I think the story on storing DNA at the scale we're talking about is not fully complete. DNA does denature and it takes a reasonably good sample to get a full genome sequence, and fully sequencing and storing data for every person has other practical issues. The article itself only references using DNA results to "prove or disprove biological sex", which is much more trivial and while it's likely to come with its own problems and edge cases, is also much less information.)