Honestly, knowing C made it much easier to understand why design decisions from Rust matter. I see Rust as kind of a (welcome) reaction to the memory model that C++ inherited from C.
Yes, I agree with the fact that learning C makes us appreciate Rust (and other safer languages) better. It's just that between C and Rust, I would pick Rust. I'm not a systems programmer, but I have worked with C before and as soon as I saw some of Rust's example codes, I liked how it taught me something and liked the design choices. Rust does seem like a nice language.