>While their emergence in a country with a well-established ideographic writing system—Japan, kanji—may not be surprising, their widespread adoption in places that had basically used only alphabets is, at least to me.
I think that western world held a very arrogant view that alphabets are somehow inherently better than ideograms. Even when we started using letters to create simple drawings that would be put inside text, most people still completely denied the possibly of using ideograms. "It's just a small fad on this small little thing called 'computer', nobody actually does this". When you stop thinking this way then it becomes obvious that, if the Japanese decided to keep ideograms, even though they already have not one but two ways of writing phonetically, then there must be some advantage of using ideograms, they don't keep kanji around just for shits and giggles.
>I wonder to what extent emoji use might evolve so that people without a common spoken language can use them to communicate with each other
I can't see this happening. The way we construct sentences makes us think of letters first, and then tune the meaning using emojis. In order for such communication to occur, we'd need to invert this process: communicate with emojis first, and then use letters on top of that. Our language is simply not compatible with that way of thinking. It's easier for everyone to just learn English.