The problem I have with people teaching C, is that there's little regard for demonstrating testing, tooling, and robust memory management. Another problem that C has unlike Rust wrt that is that Rust has most of those things built in as part of the actual language tooling, while with C you have to pick and choose between many different implementations of testing frameworks, compilers, build tools, debugging tools, memory safety tools and techniques, etc. It's both a blessing and a curse, but does make it harder to build things with C when you're just starting out imo. There is definitely a lot of history to be learnt there that is also beneficial when it comes to Rust development for sure. I guess that when you learn the hard way a low level language you find it way easier to deal with higher abstraction levels. I mean, just not at extreme levels like leraning asm.
One thing about Rust is that it's very common to use its C FFI interop layer to work with the majority of existing software written in C/C++ which will generally require a basic level of understanding of C/C++ tooling. Also, Rust's ecosystem does have all the tools mentioned above, but after you get past the Rust compiler you're basically in LLVM land and you go back to the tooling originally built for C/C++ including the linker, etc