Or create OSes where applications are all written in managed languages, and the use of GCC and clang is gate keeped to the OS vendor and native libraries, just an idea.
Bit of a nitpick, but the real value is in safe languages, rather than managed languages, no? The distinction is a little blurry, admittedly, but as an example, I figure that verified SPARK counts as safe but unmanaged.
Still niche, Rust is not up to the stuff that app developers expect in terms of tooling and D still has quite a few @safe bugs to sort out, among its current adoption issues.
Unfortunely regardless of their own reports regarding CVEs, Microsoft, Apple and Google keep turning to C and C++ for their bottom layers + managed languages, instead of going full speed in some of those alternatives.
So it appears to be the long term solution to mitigate security issues, while keeping compatibility with existing code and tooling.
Frama-C is a specific compiler. It has not much to do with proving your own code. (And C ain't a good language for writing code you want to prove correct in.)
You are right that after having proven your code correct, you might want to use an implementation (compiler or interpreter), that is also proven correct. But those are still two different things.