All of this is incredibly difficult, and an open area of research. Probably the biggest example of this approach is the Sel4 microkernel. To put the difficulty in perspective, I checkout out some of the sel4 repositories did a quick line count.
The repository for the microkernel itself [0] has 276,541
The testsuite [1] has 26,397
The formal verification repo [2] has 1,583,410, over 5 times as much as the source code.
That is not to say that formal verification takes 5x the work. You also have to write your source-code in such a way that it is ammenable to being formally verified, which makes it more difficult to write, and limits what you can reasonably do.
Having said that, this approach can be done in a less severe way. For instance, type systems are essentially a simple form of formal verification. There are entire classes of bugs that are simply impossible in a properly typed programs; and more advanced type systems can eliminate a larger class of bugs. Although, to get the full benefit, you still need to go out of your way to encode some invariant into the type system. You also find that mainstream languages that try to go in this direction always contain some sort of escape hatch to let the programmer assert a portion of code is correct without needing to convince the verifier.
[0] https://github.com/seL4/seL4