Isn't this basically the whole point of QuickCheck-like testing frameworks? They're basically a specification that is attempted to be falsified in some way by a fuzzer. I don't see why most C projects couldn't be doing this.
I think they don't do this because it's not a widely known testing method, and it's kind of tricky to implement these tests correctly.
But then again, with some dedication, quickcheck-like testing can do a huge amount of work. At work I've implemented these tests for the entire low-level IO framework for our servers and these few tests are a pure meat grinder. It triggered one severe bug that would have downed production in the middle of the night and then some more.