Are you suggesting we turn falling into a specific set of relationships between symbols an entry requirement for the Unicode database, though? How would that look like in practice? I agree you're highlighting a useful difference, but I'm not sure about implications.
Nah, I think keeping unicode as "characters" is fine. It's perfectly reasonable to encode non-linguistic data as characters if they're using in such wise.
Edit: to circle back, you said:
How are emoji different from other logograms?
No waste at all, you raised a good point :). Emoji are technically ideograms, not logograms ... though some of the Han characters are ideographic in origin/conception too (and then you get into cool things like compound ideograms), they just didn't stay purely ideographic.
Except that emoji aren't a writing system. Writing systems encode language. Emoji encode emotions, perhaps, or suggest collections of ideas/emotions, but don't convey language per se because there's no conventionally defined correspondence between words in a language and a given emoji.
If I give you a string in English or Chinese or Arabic or Amharic, using the conventional writing systems for those languages, each string will be interoperable as a specific sequence of words in that language. A string of emoji doesn't work that way.