As both a C/C++ developer with more than a decade of experience, and a Rust developer, I'll posit that if you are smart enough to master Rust, you still aren't smart enough to write safer C++. Not even close. Rust might enlighten you in some ways, and avoid you doing some mistakes in C++, but without e.g. a borrow-checker, there are still too many ways to shoot yourself in the foot in C++, that Rust would find at compile time, while the equivalent C++ code would fail at runtime. If you're lucky and happen to hit the error conditions when you test it.
Easy for you to say as a C++ developer! As someone who came to Rust as a JavaScript/PHP/Python developer, I greatly appreciate Rust checking all my work. I'm plenty smart enough to work out the problems that the compiler picks up (once I have an error message I can google for explanations and solutions), I just don't/didn't have the experience to know that my naive code was going to cause problems.