Machines with a word size that's not a multiple of 8 cannot support POSIX at all. POSIX requires CHAR_BIT==8, and to support the POSIX and C11 memory model for threads, bytes must be individually addressible without a read-modify-write cycle on a larger memory unit. So this kind of thing really is irrelevant as far as POSIX is concerned.
The lore is that the the name POSIX, not the idea for POSIX, came from RMS and was a form of disguised spite for the process (i.e. that he intended it to be read as Piece Of Shit *IX, or similar). I'm not sure whether there's any evidence to corroborate this part of the lore, but in the early days POSIX was definitely not representative of RMS's ideas/vision. These days the standards process and even the document itself are a lot more open (though still not up to RMS's standards).
CHAR_BIT==8 was not mandated by POSIX until 2001 when it was aligned with C99, and seems to have been mandated as a consequence of C99's requirement that [u]intXX_t types not have any padding bits, and the requirement (in POSIX) that network-related interfaces use uint8_t, uint16_t, and uint32_t (which, per C99, cannot all exist unless CHAR_BIT==8).
