Isn't enough money in the universe, much less the defense budget, for that.
BINGO! Security is ALL about cost vs risk management...You can always tell who the security armchair generals are....
Integrity-178B from Green Hills Software is the only EAL6+ certified operating system. But it's not suited to desktop or server use, more real-time embedded. Aside from that, the highest OS-related thing I know of in use is IBM's z partitioning system for mainframes (LPAR isolation), at EAL5.
At last estimate it would cost $10 billion to rewrite Linux. Count at least a decade and ten times the money to make a modern EAL7 desktop/server OS kernel since every single element of it must be formally designed and verified using mathematical models and proofs. I'm not even sure it can be done for a whole OS. The guy who can pull it off is a god among OS designers. I only know of one piece of software that has achieved EAL7, and it's a specialized network program.