The Gödel and computational complexity stuff is a bit out in the horizon, but the rest ain't wrong and is something that's getting a lot of (indirect) federal funding via the Secure Enclave/Trusted Execution Environment related research - and Bratus was one of the earlier people in the Trusted Computing space.

> If these folks can make safe parsers for PDF (https://www.darpa.mil/program/safe-documents) it should be possible for anything

It is, but it's very expensive. That's why a lot of this research has been getting billions in funding for 10-15 years now in order to build out the underlying ecosystem needed to harden the entire stack