Hi Andrew,
What you suggested is much more sophisticated than what I suggested. I am strictly talking about independent chains - that's all.
I am struck by the fact that the topic of "scaling bitcoin" seems to be a mix of different problems, and when people are really trying to solve different problems, or arguing about applying the same solution in different settings, it's easy to argue back and forth endlessly. Your post talks about validating transactions without seeing all transactions. This is a different problem than what I am addressing. My view of Bitcoin is colored by my experience with process groups and total ordering. I view Bitcoin as a timestamp service on all transactions, a total order. A total order is difficult to scale. Period.
I am just addressing how to change the system so that blocks can be generated faster if a) the transaction volume increases and b) you are willing to have more miners. But you are also talking about transaction verification and making sure that you don't need to verify everything. I think these are two problems that should have two different names.
Correct me if I am wrong, but the dream of a virtual currency where everybody is equal and runs the client on their mobile device went out the window long ago. I think that went out with the special mining hardware. If my organization had to accept bitcoin payments I would assume that we'll need a small server farm for transaction verification, and that we would see all the transactions. Figure 10,000 transactions per second, like VISA. As far as small organizations or private individuals are concerned, I think it would be entirely okay for a guy on a smartphone to delegate verification to a trusted party, as long as the trust chain stops there and there is plenty of choice.
I am guessing the trustless virtual currency police would get pretty upset about such a pragmatic approach, but it's not really a choice, the failure to scale has already occurred. All things considered I think that Bitcoin will only scale when pragmatic considerations take center stage and the academic goals take a lower priority. I would think companies would make a good living out of running trusted verification services.
Once again, it doesn't mean that there is a bank, the network still allows malicious nodes, but there can be pockets of trust. This is only natural, most people trust at least one other person, so it's not that weird.
Akiva