Firstly it's called bitcoin wallet and I don't think it's possible to transfer your money into bitcoin wallet  WHY NOT JUST CONVERT YOUR MONEY  IT INTO BITCOIN AND SAVE IT IN YOUR WALLET

Secondly if bitcoin is in CO-OPERATION with the banking system this might make bitcoin lose its decentralized state which makes it unique from other currencies then the value of the bitcoin and cryptocurrency might be lost. Bitcoin would not be another currency in the hands of some bodies, organisation or countries.