how do you imagine then the communication with the so-called real world for the sake, e.g., of making deposits or obtaining a loan? How can the whole system function properly without cryprocurrency banks, which are anyway somewhere on the border between the real and crypto worlds?
maybe you should list the things that you think a bank is offering but lacks from bitcoin and is required for the "functioning properly" so we can discuss them instead.
you already mentioned two things.
making deposits. deposits where? i don't get it. you control your money when you use bitcoin, you have access to them at all times and you don't need to put it with some third party and use it when they allow you.
obtaining loans? i'd say this is not a necessity for "functioning properly". there are people who never take a loan and hate doing so. and it is not a required thing in our lives. and even if needs be, you can always take a loan from someone else without a bank in the middle.