I am slightly perplexed why anyone would make a big deal about apparent non-determinism.
Even if we assume there's no noise, the underlying physics is perfectly deterministic and we are in fact maxwell's demon. Then the brain is still a stateful, chaotic system. Being stateful and chaotic would mean you could never provide the same input twice and expect the same output because its previous state would also be its input. For any observer this would look quite non-deterministic unless you had a perfect model of ever bit of information in the brain. And currently nobody claims to have such a model.
And then let's add the noise, observer effect and quantum effects back in.
So really, it's not very surprising that the brain appears non-deterministic to any physically implementable observer.
But it is not particularly surprising. Not even good old silicon-based computers are fully deterministic. Apart from intentional noise inputs (hardware RNGs) they also experience things like cosmic rays flipping bits, electrons occasionally tunneling out from capacitors or flash storage when we don't want them to and so on. Simply overclock your computer and the rate of non-determinism will go up dramatically, but that does not mean it is zero at stock frequencies, just low enough to be usable.
When consciousness lights up during a lucid dream, the sensory perception is real enough so as to be confused for the real thing. Maybe the real thing is something of a dream. When Shakespeare wrote, “We are such stuff as dreams are made of” in The Tempest, that seems to me to have been not far from the mark.
Why is that? Very unobvious conclusion.
This alongside the idea that bacteria or trees proliferate just fine without it, etc etc. This is the jist of my argument, if you want a way better analysis, please read peter watts, he is smarter than me and the work is already done.
I read Blindsight(3 times actually), and he described some end result there, skipping whole evolution process, in which that alien Intelligence (Rorschach) may or may not compete with conscious creatures.
Additionally the hypothesis that Rorschach doesn't have conscious or not managed or directed by creatures with conscious is just guess of that expedition, which doesn't really understand what Rorschach is.
From another hand, evolution on Earth demonstrates that conscious creatures (humans) completely outcompete all others.
Going with the principle of parsimony - consciousness is arguably inefficient. I recommend some Peter Watts for fun sci fi inquiry into what a technically advanced species without consciousness should look like. So why have it?
Given that nobody can answer the question of what exactly consciousness is, why it developed, and how we could replicate it, I disagree that the study of consciousness has to be "looking for something more."
If the brain is "a wet computer" (and if you have time I do challenge you to support this statement), why is it seemingly non deterministic? Or is it actually deterministic, and we just don't have the modelling technology to sufficiently grab all the variables? I think I can predict your reaction - "of course it's deterministic! The universe is deterministic, and brains are just a part of the universe!" I think that is the inevitable rational point of view, sure. I'm not saying we need to leave room for a god... I'm saying literally, nobody knows for sure. So why not study these questions?