I agree that C isn't going anywhere. COBOL is still around, and I think that at this point C is more entrenched than COBOL ever was. Not everything is going to be rewritten.
I can understand the aversion to Rust's verbose-looking syntax, but I think that the sacrifices in convenience are made worthwhile by the compile-time safety guarantees and expressiveness that Rust provides. On the syntactical level, C is simple, but the runtime behavior is difficult to reason about. This is evidenced by the countless security vulnerabilities that arise from common, but easy to make, memory management mistakes. The Rust compiler is able to eliminate these bugs at compile time, in part due to syntactical constructs relating to things such as variable mutability. Rust's type system is also stronger and more expressive than C's, which might make it more difficult to learn initially, but in my opinion it's very nice to have features like generics, instead of needing to rely on things like void pointers. Of course, it takes longer for Rust code to compile than C code, but in most cases I am fine with compile time for more compile-time safety and better ergonomics provided by the type system.
To get back to the original topic though, I think it would be ideal for C to eventually get replaced with a more modern alternative that fixes some of C's pitfalls, but I don't think it's going to happen anytime in the near future. The cost of rewriting things can be excessive in many cases (like Linux for example), and there might be no practical benefit in rewriting a finished C program that has been already formally verified (thinking of aerospace software when writing this). Also, there are platforms where only C compilers (or outdated C++ compilers) currently exist, and making a compiler for one of these replacement languages target such platforms could very well be too costly to be worth it.