We have had the examples from the banks since ancient times: denominated currency devised into useful amounts. You have a licence to print your own money. Have we not become our own banks thanks to this technology?

Begin printing BTC1 .50 .25 .125 .0625 .03125 .015625 or any subdivision you can think of, the key is that no transaction would ever need to go through the system if we exchanged barcoded paper denominations of bitcoin; like proof that you have btc in the bank redeemable at anytime over the network.

Just imagine a world where a phone is a wallet with multiple digital denominations that are simply exchanged from phone to phone; what is the transaction limit on that?