This is an example of a very thoughtful post about a very important question. I agree with your first point about "bank" as a "node" in a network of money-services.
I can see your point of view on the second point, and I agree that is a very realistic assessment of public banking institutions as they exist in the world today. I think about them a bit differently. Let's take your first point and apply it here. When I ask about public banks, I am referring to the mac-daddy of the network for money: central banks. These are the biggest nodes in the network. Although commercial banks do the actual money creation - it is the central bank which offers the greatest degree of risk to the system. Virtually no central banks are owned by the public. I think that cryptoassets like steem may enable certain people (within a network of trust) to establish a sort of public central bank to satisfy our money-services needs.
Although I mention that central and public banks have a different function but in the end they are part of the same convoluted system. Central banks take the evil to an even higher degree as their function is to actually participate directly in the economic policy of the government. Not only that but they also contribute to the formation of the same policy in a major way.
They are definitely the biggest nodes in the network - hands down.