I don't know about banks, but Satoshi designed bitcoin with an assumption early on, that all nodes mine and therefore all users mine. Later, he figured out that "nodes" would run in "server farms" and spoke about it. Of course he assumes all nodes mine there too, and everyone else uses remote nodes. Well the way the incentives are set up, eventually the only people that can afford to send transactions, barring a collapse of the value and therefore price, would be people that are 1) mining the transaction, or 2) sending a transaction to the miner that mined the block. They might collude with each other to allow each other to send free transactions, but that's not a stable state. This *is* the result of the block size limit, and a smaller block size makes success more likely, if your definition of success is a system where only miners send transactions. This is not peer to peer digital cash, but a settlement layer for sovereign entities.

But that's separate from the issue of uncapped supply I was talking about above.