The issue isn't
identity but
attestation or
assertion of identity.
The problem with DNA, as with fingerprints, voiceprints, retina scans, and the rest, is that a small sample or simulacrum of the original object or characteristic can often create a false positive.
You leave your fingerprints, and DNA, on everything you touch, literally. Your voice is now being recorded in high fidelity at great frequency, and your eyeballs are visible to whatever it is you are looking at.
The original use-case for computer passwords, as inveted by Fernando Corbato, was in a specific facility, with a physical location and at least reasonably-limited access, largely as a measure to prevent either accidental or typically prankish mis-use of other people's computer resources. The "universe" was a few score people.
We're now relaying on passwords (and numerous other proxies for identity attestation) in a universe of roughly ten billion people, with remote 24/7/365 access and highly-automated attacking systems, over a channel which provides very narrow capabilities for high-credibility, non-spoofable assertions.
For humans interacting in person, there are many simultaneous indicia of who an individual is, particularly amongst people well-known to one another: visual appearance, voice, height, gait and carriage, mannerisms, and personal/intimate knowledge. Even for in-person identity assertion, these factors break down at scale, as our primate brains can recall the features of a few score individuals, but not many hundreds or thousands, let alone billions.
(An interesting exercise is to consider the span of a year, or your life, and how much time you could dedicate to n number of people in that time. Even over a lifetime, you can only get to know perhaps 50,000 people for an hour or more 1:1, roughly a medium-sized town's population. Not even a large city, let alone a state/province or nation, let alone the global population.)
I'm coming to feel that the idea that we can transact significant interactions at this scale (population, distance, time) may well prove to be greatly flawed. Airgapping and limited access have their benefits.