Not parent but Rust definitely makes you think about a lot of important aspects of memory management like lifetimes and references and ownership and stuff. In fact, it makes it impossible not to think about them: they're enforced by the compiler.

Those mechanics are pretty important but Rust definitely lets you program with values on the heap as well, it just does it in a strongly-typed fashion. I will agree that smart pointers are generally easier to work with, particularly with things like deref coercion, but Rust is philosophically closest to a language like C++ but with a stronger type system, memory safety, and lots of footguns removed.

I think Rust gives someone a better basis for learning and writing C than probably any other modern language.