I use Rust and C at work. I quite enjoy Rust, but I currently have no reason to believe C won't outlive it, by a lot.
It also feels to me like Rust is trying to replace C++ more-so than C.
There SO MUCH C++ out there that it won't ever be replaced. For one, Rust (or plain C) isn't a good choice for big applications (GUI, video games, web browsers, and many others) where classic OOP is so useful.