I think Rust is not about safety, but about reusability. Do you like to take on a dependency on someone's code when it is in C? The answer is: roll your own code. Rust means the end of that.
Rust means software that can be written once and used "forever". Thus it enables true open source. In comparison C/C++ pay a mere lip-service, by also giving you, along with the code, lots of reasons to worry.
To be fair to C, I think C's answer here is dynamically linked shared libraries. They have lots of problems, but still they're very widely used. Even Rust programs dynamically link libc by default.
Rust means software that can be written once and used "forever". Thus it enables true open source. In comparison C/C++ pay a mere lip-service, by also giving you, along with the code, lots of reasons to worry.
This is the real innovation behind Rust.