I don't doubt your textbook correctness or the historical correctness of this, and maybe I should stress that I am not trying to exclude anyone from the bi term, but at least in my anecdotal experience, these terms are mostly used "wrongly", meaning that there is a lot of confusion. And the meanings of words change as people start using them with different intended meanings.

Therefore, given the premise that we want to simplify things by cleaning up some redundant terms, I would prefer to keep the one whose meaning is intuitively clear to everyone. I just don't see why - given bi, pan and omni all mean the same thing - one should choose the most misunderstood/misused term.

Personally, I would just keep the terms and let people choose whichever they like, I'm just trying to entertain this discussion of choosing to keep only one of them and the pros/cons for each choice.