Fuzzing has found plenty of security vulnerabilities, to be sure, but I'm skeptical that it makes static analysis obsolete. Even if it were possible to write a theoretical fuzzer that would find every possible security vulnerability, it'd still be a whole lot cheaper, and easier, to just have a tool that enforces that you write the code correctly in the first place than to spend time writing it in an unsafe language and then developing a world-class fuzzer to find all the vulnerabilities.
Totally agree that static analysis is better than fuzzing for preventing memory-safety vulnerabilities. If ffmpeg can be written in Rust without any disadvantages compared to C, then that's an easier way to ensure memory safety than fuzzing. I would be surprised if Rust can compete against C anytime soon for writing codecs, but will be pleasantly surprised if it can!
OP is criticizing without a plausible alternative; Rust is at least more plausible of an alternative. But I also suspect that C+ASM will continue to rule the day here, especially now that these fuzzing techniques are become more widespread and industrial-strength.