Computer security is a real problem that must be fully addressed at every step of the design of a system, language and tooling can help, a bit, not much.
Rust is not a "safe" language. It might be -safer- than C/C++, but only time will tell if the difference is significant.
In any serious system written in Rust, significant portions of it will have to be written in "Unsafe Rust".
You’d also have to define “serious system” and “significant portion” and if you really do mean “any,” that is, is a single counter example enough, and if not, what percentage of them would need to be so for this to be true. You’d also have to say what’s in bound or not, is it just the code you wrote for the system, is it any dependencies, etc etc etc. Does “significant” mean “large amount” or does it mean “most important”?
GhostCell is an interesting venture away from that idea. For the sorts of loopy data structures that upset the compiler, GhostCell provides a small, well-vetted, probably correct unsafe core and a safe API for accessing it that greatly reduces the amount of unsafe one should need. The core mechanism is just a higher order phantom (ghost) type parameter that gives the compiler enough information to vet that the thing you're handling was acquired properly.
The community has generally been pretty gung-ho about getting the most safe bang for your unsafe buck, and the compiler has enough bells and whistles to make many such ideas pretty seamless.