Great, I'm a physicalist so uhhhh I reject this lol. I think you can define cognitive capabilities and phenomenal experience by reducing to structure and function. You're right that it's simple though.
But the process of reduction starts by precisely defining the phenomena in terms of structure and function. If we are unable to give a precise definition that uncontroversially captures the target phenomena, then we cannot in principle give a scientific explanation of said phenomena. This is where we stand with consciousness. There is an in principle barrier to a transparent structural description of phenomenal consciousness. But this is an explanatory limit only. It doesn't necessitate some non-physical phenomena is involved. What we need are new concepts that can connect the phenomenal to the physical. But conceptual innovation is not something you get from more measurements and more data. This is what makes consciousness a philosophical problem.
Yes, reduction would be one very viable strategy. It doesn't require precisely defining the phenomenon in order for me to just say that it reduces based on the fact that reduction has been a successful approach for everything else in cognition.
> There is an in principle barrier to a transparent structural description of phenomenal consciousness.
Yeah this is what I reject. Why do you say that this is in principle a barrier? You're discussing it as an explanatory gap, not in principle.
I think it's ontological problem: structural description ontologically misses unobservable ideal substance, so the challenge is to provide a principle that would make ideal substance unnecessary. If you don't think too much, ideal substance ontologically solves consciousness, and it's not obvious how mere structural description can live without it.