Why? We already have formally verified microkernels in production (Apple's L4 variant in their security enclave, for example). I'd say the tools are mostly there, it's a matter of scaling, and maybe a matter of adapting code to make verification easier. Both things where LLMs can shine.
The biggest hurdle is probably the number of bugs in most code. Verification would mean fixing all of those as well.
Wikipedia says:
> Apple A series processors beginning with the A7 contain a Secure Enclave coprocessor running an L4 operating system called sepOS (Secure Enclave Processor OS) based on the L4-embedded kernel developed at NICTA in 2006.
Are you sure that sepOS was formally verified? seL4, also from NICTA, was formally verified, but I don't think L4-embedded or sepOS were.