Yes, that is good idea. when we have disciplinary bitcoin bank, we feel safer while trading or purchasing and we can deposit or withdraw bitcoin as like as FIAT. Now bitcoin is not yet recognised as legal currency for all countries in the world. I expect we will have a true and legal bitcoin banks for bitcoiners.
if banks have the government accept bitcoin will certainly be easier to use bitcoin, and of course security is also ensured. But when the question is bitcoin bank owned by third parties I'm not sure it would be safe