I think people are objecting to this rather extreme worse case scenario because the C library can just use the LGPL, there is no situation where it has to be full GPL. (Or else how does glibc get away with being LGPL?)
During all those years that Linux has been around, no one other than Google has tried to take this kind of material from the original kernel headers and publish it under any license other than the GPL. And no one has tried to do an alternative glibc. I guess what someone would do is take glibc and fork it on LGPL terms.
You can build libraries if you like, but you can't just put header code under a different license unless you're the original right holder or have the original right holder's consent.