Is Rust Really the Key to Improved Code, or Just the Benefits of a Rewrite?

I am a C++ developer and I am interested in Rust. There are many blogs that talk about rewriting code in Rust, which has led to significant improvements.

I don’t doubt that this is true, but is it really because of Rust? A rewrite is usually much cleaner, and this isn't something specific to Rust.

What about a completely new project? We often experiment in various directions to see what works, and requirements can change very quickly, etc.