In the past, paper currency was backed by gold. Maybe we need a cryptocurrency that is fast and cheap, but derives value from being backed by Bitcoin. It would need to be backed in such a way that it is permanent, like a smart contract or something, so that there is trust that it will never be pulled off of the "Bitcoin standard" etc.
Could Ethereum facilitate such a currency? Perhaps a smart contract that holds an amount of BTC and automatically "sells" it's currency for BTC, and "buys" it's currency with BTC, at a set rate. If you send the contract 1 BTC it gives you 100,000,000 of these units. (which can be divided to two decimal places) minus the ether fees to perform the action.
This would solve a lot of problems I think, and birth a Medium of Exchange currency that could compete with national currencies.