I don't think it's like that, since banks (although used to store money, offer different terms than bitcoin, mainly in the aspect of providing interest -stable or not- on invested amounts, while bitcoins stored offer a rise of value sometimes, but it's not like interest given almost stably mainly as a result of trading and investing the deposited money through bank professionals.
I agree with you. I do not think that bitcoin or digital currency will be a threat to banks. Especially that here in our country, banks allow to be a medium to buy bitcoins. My wallet in bitcoin allows me to buy bitcoin through banks. So I think banks will not be threatened by digital currency considering that all the cash will come from the bank.