Rust is the issue here because it doesn't give you much of an option. And that option is the wrong one if you need to do an emergency upgrade of a particular library system-wide.
It's really not, it's not hard to do a reverse search of [broken lib] <= depends on <= [rust application] and then rebuild everything that matches. You might have to rebuild more, but that's not really hard with modern build infrastructure.
Not to mention if you have a Rust application that depends on C libraries, it already dynamically links on most platforms. You only need to rebuild if a Rust crate needs to be updated.