I work on a C codebase that does this, although in the slightly weaker sense that it does drop the abstractions at a few isolated interaction points with external APIs (think openssl, linux system calls, and not a whole lot else). Yes, there is quite a lot of NIH. With essentially-uniform use of checked data structures, and an extremely comprehensive suite of automated tests getting run under ASAN (originally Valgrind), memory safety errors almost never get so far as being committed to the main branch. This is a complex, >1M SLOC distributed system that has seen several years of production use at this point, and as far as I can recall we have not seen a single memory safety related issue in production (a few have managed to to get as far as certification testing). General resouce-leak class issues have struck a few times, but are also pretty rare.
Proprietary, naturally, so I can't actually show you (sorry), but it absolutely can be done in practice. It isn't even really all that difficult, it just needs to be done from the start, and then you just need a bit of discipline to keep it up.