I'm totally aware that C++ has unique_ptr which can give you something relatively comparable to the Rust memory management, but I personally think that if the compiler doesn't have any kind of official idiom on the subject, it'll probably end up in the codebase. C++ kind of prides itself on being able to "write however you want", which is fine, but then that means that people might start using raw pointers, unchecked arrays, and mutation.
Could a vigilant C++ programmer replicate every feature of Rust? Absolutely, not denying that for a second. Rust doesn't give you anything as much as it enforces a paradigm.
At least that's my two cents.