In fact, such an effort was started at AT&T back in 2001. The language was named Cyclone [1]. It met its 1.0 release in 2006. It has since been abandoned. Which is a damn shame, because it looked like it had real potential.
Is C a primitive language? Yes. In fact, it's almost stupidly simple compared to most modern languages. But its greatest weakness also proves to be its greatest strength. The main cognitive overhead from using C is in its manual memory management model and certain gotchas in standard libraries. It being bare bones as it is (but not too much) also makes it surprisingly pleasant at times. I get the feeling that plenty of modern languages try too hard to be novel and, for all the freedom you get from not having to worry about anything below program logic itself, you still end up expending a lot of effort into complicated high-level patterns that are frequently interspersed with arcane PL theory.
But that's not even the main reason why something like Cyclone is much needed. No. It's that we've pretty much perfected a ton of our APIs, like POSIX, to work with C. It simply feels most natural to work with POSIX in plain C. FFIs and bindings vary, some of them like Nim's actually feel quite clumsy (otherwise Nim makes it absolutely trivial to create FFIs, which is great).
Finally, refactoring 30 years worth of code into Cyclone sounds far more realistic than rewriting the world in Rust.
[1] https://en.wikipedia.org/wiki/Cyclone_%28programming_languag...