I work on (well, mostly near) an extensible C compiler, designed so extension authors can independently create extensions, and users can import them as easily as libraries: https://github.com/melt-umn/ableC/ (and I'd love to answer any questions you have about our approach or code.)

IMO this approach hasn't taken off because maintaining compatibility with C while adding safety (or really just about any property) means implementing your own sublanguage that can't arbitrarily call C functions while maintaining your safety properties. On the other hand, C being able to call into your sublanguage easier is a benefit versus jury-rigging Cargo into your build system (in the case of Rust).

On the other hand, this approach works great for adding extensions that increase the expressive power of C with new abstractions, for example algebraic data types, C++-like templating, etc.