With password/payment/location breaches you have the ability to change what you entered as to invalidate/outdate the data which was stored.
Having your biometric/genome authentication data stolen or made public will be a nightmare.
There's no practical way to protect our genomes in meatspace. We're constantly shedding DNA into the environment. Hair, skin, saliva, etc. For example, an adversary can just tail us to a coffee shop or restaurant, and take a utensil or straw or napkin that we've used. And then submit the sample using a fake name, as investigators often do.
Edit: Those are excellent comments about scale. But generally, if you don't want to publicize your genomic data, just don't send in a sample.
INSERT INTO Citizen(dob,ssn)
VALUES 2030-10-28, sha(atgcaatgcatcgc..)