Software like glibc is battle-tested---it is _widely_ used on hundreds of thousands of systems around the world, and has been used (though not at today's massive scale) for decades. I understand that glibc is under active development and there is a lot of new code, but let's keep this in perspective:
Writing a new implementation of a system is a huge opportunity to introduce bugs. There is focus on these specific problems, but in the broader scheme of things, glibc is remarkably stable, performant, and feature-rich. A new implementation will have bugs, and those bugs might be less likely to be caught simply because the system will not be as widely used for quite a long time. Even formally proven systems don't address flaws in the actual program specification. (See "The Limits of Correctness" by Brian Cantwell Smith for a good discussion). Also relevant (which I'm reminded of in part because of his recent death): Peter Naur's Programming as Theory Building.
So even _new_ code to glibc has the benefit of a huge community of both developers are users to eyeball it and test it out in production on a huge number of systems.
So rewriting glibc may solve certain problems, but it's bound to create a whole lot more, considering the narrow range of issues that are being focused on. New Rust code will have undiscovered issues too, even if they're not memory or stack related. I feel that this effort might be better spent fixing and finding problems with glibc---and continuing the development of tools to find those problems, to benefit _all_ of our old C libraries and programs---than rewriting for the sake of rewriting.