You state that the CAP theorem is fundamental to all of what you are describing. The CAP theorem is essentially this:
a statement that it is impossible for a distributed computer system to simultaneously provide all three of the following guarantees:
Consistency (all nodes see the same data at the same time)
Availability (a guarantee that every request receives a response about whether it succeeded or failed)
Partition tolerance (the system continues to operate despite arbitrary partitioning due to network failures)
Let's start with an assumption that I agree with the CAP theorem, and further assume that this notion is actually correct.
In that case, let's say all nodes don't see the same data at the same time. Seems reasonable, after all, how could they?
The problem manifests as an inability to reach consensus on which of the conflicting Partitions has the accepted and rejected double-spend. You might start reading roughly page 27 of this thread to see the discussion between enet, monsterer, and myself, wherein I elucidated this.
Availability - for the sake of argument, let's say every request receives a response about whether it succeeded or failed, or if it doesn't the first time, it is programmed to repeat the same request until it receives a reply, which it will receive within a reasonable period of time.
Inaccessibility manifests as a protocol requirement to prevent interoption between Partitions to solve the Inconsistency mentioned above.
Indeed centralization of policy (thus abandoning decentralized, permissionless commerce) is the only way to deal with the Inconsistency or Unavailability (choose one) when multiple Partitions are allowed.
I have argued upthread that centralization will be the only way Iota (with its multiple Partitions) will avoid divergent, chaotic Inconsistency (since obviously it doesn't limit Accessibility).
So under these conditions as described above, which I suggest are roughly representative of the actual condition of bitcoin (as an example) at most times, then it would seem to me that despite the presence of the CAP theorem, the system continues. Why? Because the system is dynamic, not static.
Bitcoin continues because it doesn't allow multiple Partitions and because in the case where chaos would result from a fork, then centralization of the mining is able to coordinate to set policy. But we also see the negative side of centralization when recently the Chinese miners who control roughly 67% of Bitcoin's network hashrate were able to veto any block size increase. And lie about their justification, since an analysis by smooth and I (mostly me) concluded that their excuse about slow connection across China's firewall is not a valid technical justification. Large blocks can be handled with their slow connection by putting a pool outside of China to communicate block hashes to the mining hardware in China.
Possibly for systems that are very fragile or inflexible then I think that changes in these C-A-P conditions could cause them problems, of varying degrees of seriousness. But even for highly centralized systems (e.g. corporation-states), which are highly resistant to change, they are curiously persistent. This may be because of people's desire to perpetuate an institutional memory and cultural history of organizational (and national or tribal) ideology. Belonging to a large group - identity which conveys a larger sense of belonging - has been, for good or for ill, branded into the human psyche. War, government failures, economic disasters, mass murder - nothing seems to stop the bulk of people in society from falling into the trap of the state, again and again. But I digress. What about those decentralized systems? Does the issue of the CAP theorem necessarily mean that they can't work?
Not necessarily. If a system is dynamic enough, and is managed well by its community (however that needs to happen with a distributed system in order for some degree of balance to be attained between a "centralized" development structure and a "decentralized" system, as no system is ever 100% "decentralized," then a well-cared for decentralized, distributed system can be continuously propagated (or re-propagated, much like a plant's seeds are used to regrow the fields).
This noise is what happens when smart people haven't studied an issue in depth and start going off on conceptual abstractions in their mind without really understanding what they are conceptualizing. I hope my explanations above have caused you to realize you are incorrect.
Interesting discussion though!
Thanks. Hopefully you will read it all.