I find that the best way to read the term "emergent" is to regard it as connotationally meaning "oh crap, this is too complicated for me". Systems with easily-understood high-level behaviors, like the avalanche, meet most usual definitions of emergence but are rarely described as such.

e.g., intelligence as an emergent property of neurons = "Oh crap, intelligence is too complicated for me".

This helpfully moves the word from being a somewhat hand-wavy category to being an objective statement of lack of comprehension. For instance, I can now unambiguously state that I consider intelligence to be emergent, while being happy to have Eliezer disagree.