What's in a Standard?
The Single UNIX Specification contains a lot more than just a set of C functions. In particular, it specifies a large range of userland utilities that must exist. Many programs depend on the existence of these utilities, via shell scripts or other invocations. The majority come from the GNU coreutils package. Again, in terms of code size, coreutils is of comparable size to the kernel.
It's easy to discount coreutils as being an unimportant part of the operating system, but that perception is misleading. Without the core utilities, most init scripts won't run (even with Bash installed), rendering the system unusable. Most installers won't run, meaning that you can't install any other programs. Even basic functionality such as copying files is provided via these programs.
SUS provides a list of 175 utilities that must exist on any UNIX system. Most of these utilities (with some exceptions, such as vi) are provided by the GNU Project in a common Linux distribution. Some of these utilities aren't used by the average desktop user; for example, the standard requires that the system include c99 and fort77 utilities for compiling C and Fortran programs (both are provided by GCC).