I agree. The terms and the distinctions themselves do not make much sense. The only one of these that I ever use with students, and that just to fill them in on the crappy terminology, is Hs. The others are confusing and worthless. There are many examples of peculiar terminology in celestial navigation, like "horizontal" parallax (is it sideways?), and "semi-diameter" (not radius?) and even "declination" (what's declining??). But these are historical terms that reflect the legacy of the development of navigation. They deserve a little respect, if only for historical "color". The acronym-happy late twentieth century has buried us in two-letter and three-letter shorthands that obscure rather than illuminate. Babbling about EP and AP and GP and all the rest isn't communication. This private, occult, semi-military jargon has become an unintentional barrier, a rite of passage with no educational purpose. I say, 'ditch it'. To which I should add a disclaimer: "IMNSHO". Ha!
To me the terms for height make sense. Hsextant or Hobserved both contrast well with Hcalculated in the final step determining offset to make it clear what you are talking about and since the first reading comes straight off the sextant, Hobserved logically becomes the final result on the obersvation side of the process. The naming of intermediate values is a bit arbitrary but something had to be picked to make discussion of the process easier.
I disagree about the acronyms and jargon. While it may be an impediment to entry, in the long run jargen and special words provide greater understanding of the topic. In general having a word for something actually makes it easier to think about. In some cases having a word for something actually make thinking about it possible. This is related to "Theory of Mind" if you want to look into this deeper.