A lot of the disagreement here comes from what kind of emergence people are talking about.
Most philosophers are perfectly fine with weak (scientific) emergence. Temperature, liquidity, elasticity, traffic jams, economies, etc. all emerge from lower-level interactions. They’re not properties of single particles, but once you understand the micro-story, there’s nothing mysterious left over. Crucially, all of these are structural or functional properties, describable entirely in third-person terms.
The worry about consciousness isn’t really about complexity. It’s about the fact that consciousness seems to involve an experiential aspect — there being something it is like — and critics argue that this doesn’t follow from structural or functional descriptions in the same way temperature or liquidity do.
Similarly, when people say “you can’t open the skull and point to consciousness,” they’re not making a naïve spatial claim. The point is that no amount of third-person description of neurons, firings, or networks seems to capture or entail first-person phenomenal qualities like pain or redness.
So you see, consciousness isn’t treated as special because it’s complex, but because it seems to introduce a different kind of property — phenomenal experience — that standard emergence stories were never designed to explain. Whether that really is a problem is exactly what the debate is about.