It also feels to me like Rust is trying to replace C++ more-so than C.

There SO MUCH C++ out there that it won't ever be replaced. For one, Rust (or plain C) isn't a good choice for big applications (GUI, video games, web browsers, and many others) where classic OOP is so useful.

Maybe "replace" was the wrong word. What I mean is that Rust is "a better C++" to a much greater extent than it is "a better C".