I understand your pain(and also have very similar pain when English words were put into katakana) but for that example, it does make sense as for native English speakers, my assumption was that the emo- part of the word came from emote. https://www.merriam-webster.com/dictionary/emote https://en.wikipedia.org/wiki/Emote
The “e” is from 「絵」and “moji” from 「文字」, transliterated as 「えもじ」, “e” + “moji” gets you “picture message”. It was a stroke of luck that it was similar enough to emoticon to neatly fit into our existing lexicon and be understood at a glance by an English speaker, at least the gist of it. A picture message is a little bit different than an emote icon if you think about it because there’s many more pictures which are not emotes per se, but can be used within a message alongside the emoting emoji. :)
Honestly it kinda does. I wince every time I hear emoji pronounced like いmoji (where the e rhymes with tea) instead of えmoji (where the e rhymes with meh), or pluralize Japanese nouns (“emojis” “sushis”). That said, this is a me problem. People are going to pronounce words in whatever way makes sense to them, where the emphasis goes, how it is pronounced, which vowels get emphasized or contracted together will change over time. There is a reason we don’t all sound like Elizabethan-era Englishmen when we speak English.
Even proper nouns such as names get adapted. How many different variations and pronunciations are there for the name “John” in Europe?