Can it though? Paper wallets and USB drives, sure, but metal plates? DNA decays pretty easily unless you go through extensive measures to preserve it and even then it will become unusuable within a couple of millions of years. I don't see how a private key written in metal or stone couldn't outlast a private key written in DNA. Even the size advantage of DNA is moot based on the need for infrastructure to keep it somewhat stable.

What I love about this concept though is that it opens up the possibility of storing arbitrary data in living beings. If we find a way to keep the payload safe from mutation we could encode any sort of information into generations of future lifeforms. Probably not private keys though, because the data would be pretty much public.