Would the full phrase "memory safety/thread safety" have been something more gentle to your ears? Because memory safety has been a metric used to gauge software for as long as I've been alive and then some. If a program I write is correct on its face, but subject to issues caused by asynchronous reads/writes (perhaps completely unexpectedly), then it is not memory safe and will still cause problems. Whether you consider this a separate quality than correctness, or as a subset of correctness, it's still a useful metric to employ.
In my experience, lack of memory safety is one of the largest sources of non-trivial bugs I experience. Sure, if you are writing truly mission critical software for planes or pacemakers, you are going to need stronger (and different) guarantees. But Rust's goal is not provable correctness in the Coq sense. It's to provide a productive interface for designing efficient and memory safe/thread safe programs.
In my experience, lack of memory safety is one of the largest sources of non-trivial bugs I experience. Sure, if you are writing truly mission critical software for planes or pacemakers, you are going to need stronger (and different) guarantees. But Rust's goal is not provable correctness in the Coq sense. It's to provide a productive interface for designing efficient and memory safe/thread safe programs.