I think Rust is a bad example, but I think the general idea that the design of a programming language can help with the weaknesses of LLMs makes sense. Languages with easy sandboxing (like Deno where workers can be instantiated with their own permissions) or capability-based security could limit the blast radius of LLM mistakes or insecure library choices made by LLMs, while also giving similar benefits to human programmers and code reviewers.
Why is Rust a bad example? Of the code bases I've tried Claude on so far, it's done the best job with the Rust ones. I guess having all the type signatures there and meaningful feedback from the compiler help to steer it in the right direction.
Rust doesn't protect you much further than most typed memory-safe languages do; it won't stop an LLM from writing code to erase your filesystem or from importing a library that sounds useful but is full of malware.