I think that a lot of the time, the attempts - whether conscious or unconscious - to create a Trinary are because people are reluctant to accept a system which appears boundless. It's the same reason people get uncomfortable with micro-labels.

(It's a little like when you take the cat to the vet and they won't come out of their carrier, despite how difficult it was to get them in there in the first place. ...I have no idea where my brain got that analogy, but I kinda like it!)