I don't see by what Logic you think that a Sufficiently Complex System even only just might Achieve Consciousness. There is no Maybe or Might about it. It is an Incoherent proposition, both Logically and Scientifically. What is it about the Complexity of anything, that Logically makes you think Consciousness will be achieved?
The "logic" is that all we have evidence for is a rather complex mass of atoms called the brain, with a rather complex web of interactivity - the working brain is the most complex thing are aware of. By a long way. The evidence is that whatever the brain produces (e.g. consciousness, experience) is because of what is going on within the brain, the interactivity therein. Destroy brain, destroy that complexity, here endeth consciousness. Disrupt certain patterns of activity: disrupt experiences, disrupt even conscious awareness.
The evidence is that a single neuron firing displays none of what we would call experience, consciousness etc. Therefore the "logic" is that those things (consciousness, experience et al) arise due to the complexity of the interactions.
Now, as to why a sufficiently complex system
might, rather than
will: I have sufficient funds to buy a bottle of vodka, but that doesn't mean it will happen.
But the real issue goes even Deeper. I like to specify particular aspects of Consciousness because Consciousness is not a very clear concept in the first place. I try to study aspects of Consciousness, like the Experience of Redness, the Standard A Tone, and the Salty Taste. So how do you explain these Conscious Experiences simply by virtue of Complex Computations or Processing?
The real issue doesn't go deeper. You can pick elements of consciousness or experience to focus on, but that doesn't make the real issue deeper.
As to the question, my answer - and probably the answer of every scientist: beyond it logically being an emergent property, I don't know. And that lack of knowledge is not sufficient grounds upon which to cast aside the evidence and logic.
Now, you don't have to accept either or both if that is your desire, but other than your personal incredulity, you haven't yet offered anything other than trollish dismissal.