I think historically ANSI did languages.
But, I don't know specifically why IEEE became the standards body for POSIX. I did participate for a while in the IEEE standards process (not POSIX, but something else), and I knew it as a large, very active, well managed organization, always eager to take on new things (such as the thing that I was engaged in). So maybe that was one reason.
Maybe a greater reason is that the part of IEEE standards that did software was chaired by a person from DEC (forgot his name). I'm sure DEC had a strong interest in a UNIX-based standard, if only to make sure that it didn't go completely wild and negate DEC's huge head start in selling machines to run UNIX.
Marc