Very little of any software "has to be" written in C anymore.
Entire huge games have been shipped with no C in them, for example. Of the things you listed, the C implementation is usually for compatibility with non-C languages, not to espouse C directly!
I have an entire language and compiler toolchain written with 0 dependencies on raw C. It has support for speaking the C ABI, but that has nothing to do with the C language being a mandatory component of anything.
The pieces of software that are in C are usually some of the most hardened and well-tested portions, for several reasons - not least of which being the fact that they usually exist to interface with non-C languages.
The effort of rewriting C code into Checked C is nontrivial. The reward is marginal at best for already-bulletproofed code. I just don't see a compelling reason for adoption.
It's a nifty project from a languages standpoint, but I don't see it being revolutionary.
And of course, if it "has to be" written in C, you cannot write it in Checked C.