Large, complex code written in C that has a wide API footprint will work with little or no modification among systems like GNU/Linux, Solaris and Mac OS.
The specification is online and people use it when coding, refer to it it in discussions and when filing bug reports.
2018 edition: https://pubs.opengroup.org/onlinepubs/9699919799.2018edition...
It's been my experience that the maintainers of major FOSS projects take it seriously when something is reported as being at odds with POSIX.
I don't remember any recent "POSIX strictness battle"; you didn't just make that up, did you?
There was as struggle starting in the 1980's to deal with incompatibilities among large numbers of vendor-specific derivatives of Unix that were cropping up everywhere. Unix brand incompatibilities negatively affected the users, who wanted their programs (and skills) to transfer. That is more ancient history. In retrospect, it looks like the standardization effort was broadly successful.
POSIX is not exactly standing still; it has been amassing new interfaces, and vendors adapt them as specified.
When I started coding in Unix, gethostbyname was the way to resolve DNS; now you have getaddrinfo, which is more generic and can give you IPv6 and IPv4 results in the same call. Even in basic Unix functionality, there are new features: for instance, various "at" functions, like openat: open a file relative to a specified directory descriptor, rather than the current working directory. POSIX specified threads that work everywhere, shared memory that works everywhere and other things.
There is rather a struggle between "use latest stuff in POSIX" versus "have code work on older systems".
But, overall, POSIX is a huge relief.
POSIX is a big reason why you can take code written using Glibc and get it running on Musl. Or on Cygwin.
An alternative C library that has Glibc compatibility as its goal would be a lot more difficult to develop if it had to be based entirely on reverse engineering Glibc. The Glibc documentation isn't complete enough. (And, doh, that's because it expects you to refer to POSIX for the details.)