Apologies for a late reply. I am basing my approach not on Big-O analysis, but on direct experience in distributed networking — and also the experience that most participants are blind to tragedy-of-the-commons issues that arise in distributed networks. You might want to have a look at the history of network-level scaling issues in file-sharing networks, if you are interested in the technical side of it.
I understand your chunking analogy, but I don’t agree with the idea that public free-for-all blockchain-based systems are the right tool/medium to solve the trust issues. If you look at market/trade systems in any well-developed MMO out there — they work just as well, and require a fraction of resources. I think the conceptual binding of smart contracts to public blockchains is the most unfortunate thing that has happened in public perception of IT in the last decade, because of the amount of resources that have been consumed by this idea (and I include the brain power of the developers working on this.)
My main argument is that the cryptocurrency networks as they are practiced now only look plausible, as long as the participants only look at individual challenges, and not at the system, ie at the combination thereof. As long as you only look at it from the societal perspective, and ignore the technology, it might seem like a good idea. If you only look at each technical problem in turn, they are all solvable. But not in combination, because Trustless, Secure and Scalable in distributed systems are, in my opinion, mutually exclusive: only two of those work at a time. I have yet to see this proven wrong.