There are pieces of software that should be given priority for a rewrite in Rust, but most of C software is never going to be rewritten, because there is simply too much of it.
Therefore, even if C did not have any advantage of its own over Rust, there would still be legacy software to maintain and to extend.
The advantages of C include that sometimes, an embedded processor with a proprietary instruction set is provided by the chipmaker with its own C compiler, which is the only compiler supporting the instruction set; that C is still currently used to write the runtimes of higher-level languages (I'm familiar with OCaml, but it isn't too much of a stretch to imagine that the runtimes of Python, Haskell,… are also written in C).
I sincerely hope this is not the general attitude of the standards committee. Some of us actually prefer C, and would like to see the language continue to flourish.
It goes deeper than that, in a couple of places Rust depends on the C standard: the fixed-layout `#[repr(C)]` structs (without that attribute, the compiler is free to reorder the struct fields; with that attribute, it's laid out the way C would do it), and the `extern "C"` function call ABI. The way to call any other language from Rust, or Rust from any other language, is to go through `extern "C"` functions passing `#[repr(C)]` structs. So even if the C language dies one day, parts of it will live in Rust forever (or as long as the Rust language lives).