> The argument seems to be that beyond a certain level of complexity you'll somehow automatically get consciousness.

I agree with much of what you say but not with this statement. That would be a silly argument since it's very easy to imagine algorithms of arbitrary complexity that are trivially not conscious. A better argument for computationalism states that (1) consciousness could be an emergent property of certain algorithms when they are running on a computational device, and (2) among all known explanations of consciousness, a computational theory seems to be the overall best theory, especially if compatibility with contemporary physics is a goal.

The article lays out one incorrect standard argument against (1) that basically just says that it's hard to imagine (1) and therefore (1) is not possible. The Chinese room and the Chinese brain arguments do the same, and they are equally flawed. Just because something is hard to imagine or comprehend doesn't imply that it isn't the case. In fact, if consciousness is an emergent property of certain algorithms when they run, then it is clear that their workings are hard to understand. That's reasonably clear because otherwise we would already have found them.

Regarding your worry that we might not be able to detect consciousness: I agree with that but there is, interestingly, a loophole. At least in theory it could be possible that if computationalism is true, then we can determine that an algorithm produces consciousness by mere analytic insight. Again, this is hard to imagine, but it is not impossible. It seems more likely that (2) is the only route to go, that for some reason we lack the capacity to determine consciousness reliably by mere analysis, but we don't know.

(2) is the most controversial in the philosophy of mind. On the one hand, it is clearly inference to the best explanation, and there are various methodological concerns with such arguments. One might claim that they have no justificatory value on their own. On the other hand, the alternatives to computationalism really are way more mystical. The brain could be a hypercomputer. But hypercomputers can also compute, so it's just an extension of computationalism and it is not even fully clear yet whether and which types of hypercomputers are physically possible. Then there is Penrose's theory of quantum consciousness, which basically just attempts to explain one mysterious phenomenon by another mysterious phenomenon. At least it was designed as a falsifiable theory and therefore is scientific. Finally, we have all kinds of non-computationalism that are mystical, explain nothing, and lead to strange homunculus problems. The worst offender is classical dualism. Dualists reject physicalism and often incorrectly assume that computationalism presumes physicalism. Ironically, however, computationalism would also be the best theory of how the mind works if dualism was true. The dualist just adds to this various stipulations that are incompatible with contemporary physics.

> Because the experience is subjective, you can't just assume that behaviours that appear conscious are proof that consciousness exists.

That's only true from a very narrow scientific perspective. Psychology allows the use of introspective data, so from that perspective subjective reports about consciousness (or related feelings and states of mind) can be valid data. Using a reasonable definition based on introspection we can even determine different degrees of consciousness and study what's going on in the brain while they appear to be active. Typical examples: falling asleep, dreaming, sleep paralysis, research on anaesthetics and mind-altering drugs, various forms of physical brain defects, the study of coma patients, etc. In a nutshell, I don't really buy the "consciousness cannot be measured" argument. What is correct is that we cannot show conclusively that another person or machine is conscious, just like we cannot disprove solipsism. But this is best treated as an overly skeptic philosophical argument, and at best this would support the theory that consciousness is an illusion and we are nothing but unconscious robots. That theory is not very plausible either, so we should be ready to grant consciousness to others based on introspective data.