I trust bank now and for a while until there is a better and clear better option. We can transact yet without banks. For now the whole world is still ran by fiat currency hence we can't let go of banks yet. But probably when the whole world adopts bitcoins then we could all be our banks. Then we can just move on and forget banks and financial corporations.
According to banks are idiotic business, where the banks use to loot common people money by the name of fees and penalties. However Bitcoin is completely different just only fee for the transaction. Other than that everything different than banks.
Yes when people are realizing the benefits of using bitcoin wallets instead of bank system, they will slowly stop using banks. From that point people will not keep on trusting banks. That is the reason people are saying bitcoin will replace banking system. In my opinion too it will be possible and it is going to happen very soon.
Two reasons bitcoin is never going to "replace the banking system." 1) Transaction fees will soon be unwieldy for bitcoin, and 2) banking system provides too many other functions to be replaced by a digital currency.
Bitcoin fees are rising. Every halving and with the more congested the network gets, fees increase in nominal bitcoins. On top of that, the more valuable bitcoin is in USD, the more those transaction fees are. We're currently on the edge of where bitcoin is not competitive for small transactions. Paying 50 cents to buy a $10 item with bitcoins is not economical, considering you could buy the item with digital fiat with no extra charge.
Also, bitcoin is not condusive to credit. Lending and therefore economic growth would seize up in a bitcoin denominated economy. People expecting bitcoin to replace the USD and create an economic paradise are delusional.