interesting idea..
however the banks operate under a fractional reserve system. Say you have left your hard earned cash in a deposit the banks go and lend that money to someone else.
Its highly possible that you could one day try to withdraw you money and they will turn around and say we don't have it. In any other industry this would be a CRIME!!
Crypto currencies are backed by the proof of work and proof of stake miners that expend electricity or resources to secure the blockchain.
Compare this to the USD in which the US government has a 20 TRILLION dollar debt and keeps paying its own debts by creating money out of thin air. Again this would be illegal in any other environment.
I know which method I put my faith in.
http://www.investopedia.com/terms/f/fractionalreservebanking.asp
http://www.usdebtclock.org/