Or 2 - the conscious reflective self is more like a saccade of attention moving between various systems operating according to its overall supervision.
I think two makes much more sense, since we don't observe the actions of others to be random or inconsistent (in ordinary circumstances), no matter how quickly they're responding. If George is on edge, and we throw a ball at George, George will do what he generally does - flinch, react with anger etc. George won't catch the ball perfectly in contrast with his emotional state. If Sue sees a famous criminal on the street, Sue will generally react as Sue would be expected to based on her priors - scream, run, freeze etc. Sue is unlikely to smile and raise her hand for a shake. Circumstances where we and others deviate from the 'reasonable' instantaneous response are rare, comical and associated with inattention, distraction or visceral symptoms (like illness). Therefore either we presuppose another personality operating at a preconscious level - or we are queuing classes of responses that make sense on some general level, even if they occur too fast for linguistic reflection or 'conscious' perception.
The language example in the comment above is a great reflection of this. We are able to carry out coherent, situationally appropriate conversation including symbolic reasoning. So I'm not sure what kind of conditioned mechanism or second personality is supposed to be responsible if consciousness is eliminated.
I am completely unfazed by the fact that what I intuitively thought the process might have been isn't the real process. The entire history of science from start to finish has been the unrelenting story of taking a closer look at something than we ever have before, and being surprised by what we found. The exceptions to that, such as predicting antimatter or the Higg's boson, are notable stories precisely because they are exceptions. Nevertheless, those surprises never negate our previous experiences. They reveal unexpected sources and surprising nuances, but the fact that we were surprised by where our higher-level concepts came from reveal that our previous understanding was in error, not the higher level concepts. Water has been wet for the whole of human experience, no matter whether it was its own element, or a essence, or a composition of atoms, or a pattern of fluctuations in quantum fields, or whatever the final Grand Unified Theory might declare it "really" is. Our understanding of water has been greatly enhanced by those advances, but it remains wet.
Nevertheless, my self is whatever is making decisions. The only way to break me off that definition would be to remove the entire "making decisions" part, which gets into its own philosophical thicket. Even in a fully deterministic universe I may still be "making decisions", despite popular belief to the contrary; one must simply be more careful about the definition of "making decisions" but meaningful definitions can still be produced.
There's a very long history of this sort of word chopping. Declaring this or that thing an "illusion" simply because it isn't exactly what we thought it was, or because it turns out not to be an atomic object of its own in the universe (hardly surprising since the only atomic things that seem to actually exist in this universe aren't very philosophically exciting, like quarks and electrons) is one very common tell, but it's not the only one. Consciousness gets a lot of stories like this where someone tries to manipulate words to "reveal" conscious experience is some sort of fake or something, but amazingly, not a single one of them has affected my own personal conscious experience. Per Descartes, as the existence of my own conscious experience is arguably the single thing I have the most confidence about, arguably the only thing I am 100% certain of, I find myself rather unimpressed with attempts to deny it. The fact that a certain subset of scientists are perturbed by their inability to wrap numbers around it is their problem, not mine. They are welcome to try to explain it; any attempts they make to explain it away can be discarded without further examination.
I think you’re missing the point. If you just define away “self” as whatever turns out to be making decisions, then sure, you can claim to never be surprised by anything. If we literally discovered that all your decisions are being made by a physical computer in a laboratory and instructions are sent to your body with radio waves, you could just say “well that’s what my ‘self’ is by definition, so this isn’t surprising at all.”
Of course, when I phrase it so baldly, you might be inclined to say "Well, of course", in which I would suggest, apparently you are agreeing with me. But this slight-of-hand occurs a lot, when you aren't so clear with the statements.
This is only a challenge to "anyone who places a lot of importance on that feeling of identity" if they placed all their importance on secondary opinions of what that identity is. Don't do that. Your identity should not be tied up in "I'm a conscious being because my neurons in my hemidimi cortex fires and directs my globocampus to plan how to start moving my finger", because then you have an identity crisis when it turns out "hemidimi" and "globocampus" are just made up concepts with no referents in reality. But there's a lot of people who will get very excited or try to get you very excited when it turns out they disprove the existence of hemidimis and globocampuses and declare this is all deep and profound and stuff. It's not. It was an error in the identity, that's all, but you're still a conscious being.
So, yes, I'm disagreeing. This isn't profound at all.
Or at least, it shouldn't be, if you aren't making fundamental category errors, if not outright reveling in fuzziness and uncertainty.