Would it be a good idea to rewrite glibc in Rust?

Rewrite the C standard library in Rust? I'm not sure I understand how that even makes sense. Are there problems this would solve?

A C standard library rewritten in Rust already exists. [0]

glibc has its share of CVEs, and many of the bugs are of the double free, use-after-free, buffer overflow variety. [1]

[0]: https://github.com/redox-os/relibc [1]: https://cve.mitre.org/cgi-bin/cvekey.cgi?keyword=glibc