The efficiency and explicit memory ownership in Rust makes it a lot easier to avoid some of the scalability problems you run into in dynamic languages. The amount of material you can find online on people discussing hunting down memory leaks in Rails, or discussing how they just scale up by throwing gobs of RAM and extra servers at the problem or restarting their app every day or two, is all stuff that is much easier to avoid in a language like Rust. It is possible to leak memory in Rust, but due to how explicit you are about how memory is owned, it's less likely and more likely to be easier to track down if you do.
It is a bit more conceptual overhead to learn Rust than many dynamic languages, but I think that overhead is well spent as it can pay off in performance, stability, and maintainability later on.