Am I the only person who still calls "ASCII emoji" "emoticons"?

No, you're not. :) Emoticons aren't emoji.

What would an emoji provide over that ascii combo?

Variety and reduced ambiguity.

Nuance

The opposite of nuance because the image renders differently for different browsers/platforms so you can only assume a very vague meaning.

I agree on the assuming and the vagueness. Kids these days feel that the thumbs up emoji is like a passive aggressive middle finger, same with a green checkbox -- and they are apparently bothered by the ellipsis too while we are at it -- not understanding that it is totally valid punctuation and what it can represent. The fact that these individuals are absolutely wrong comes from the pictograms being vague.