Then when the user inevitable loses their private key? Not everyone is tech savvy enough.
Faking DNA; well for that it would depend on how the test was administered. A cheek swab would be reasonably easy to fool, a blood draw less so if administered carefully. This is all assuming no corruption or anything; DNA tests contain no cryptographically attestable proof of match.
Any who knows, with DNA based therapies you might find yourself unable to pass a DNA test for yourself in the future.
In contrast, if you have public-key encryption people are going to build systems on the assumption that your private key is only available to you despite several decades of history showing that's not a safe assumption.