"Long before retail banking had started, there was a very rich city person in a kingdom where people exchanged gold for food, and other useful commodities. His name was, lets say, Mr. R. As he was so rich, people use to borrow money from him from time to time after agreeing upon collaterals. Mr. R was very happy with the way things were running, because whenever there was any adverse natural calamity, the poor guys (who lets say depended upon farming for their survival) failed to pay him back the stipulated loan and thus Mr. R would own the promised collateral.
Some time later, it so happened that there was favourable climate and all the borrowers paid back their loans and Mr. R didn't get any cheap collaterals. He was frustrated because he was not gaining anything out of his efforts in lending the money. He said, "Let me charge them an additional amount for using my money !". This was the birth of interest rates.
One can very easily imagine, Mr. R demanding more interest from a person who has a weak collateral and lesser from the other."
I guess the above story forms an important link in the thread which I am about to propose. However, before delving into this further, I want to make the following disclaimer: The following discussion is primarily for academic/discussion purpose and has no relevance anyhow to my professional output.
To start off, imagine a hypothetical world, where everyone is completely truthful, trustworthy(I hope truthfulness and trustworthiness are equivalent but am not completely sure), and rational.
If this was the case, my claim is that we can do away completely with all the banks and have just one central bank.
The intuition behind this is the following: Lets say there were only 2 people in the whole world, namely Mr. A (car manufacturer) and Mr. B (wants to buy a car). Now, B earns money, saves it till he has the amount to buy the car. A takes the car money from B, and manufactures the car for him and delivers the car to him after some days.
We all know the reality: B earns money, saves it or invests it (earns interest on it). A takes a loan from a bank, constructs the infrastructure required for car manufacture and keeps paying interest to the bank. Finally, on the day, when B has the required funds, A gets the money, pays back the loan and B gets the car. If A would have trusted B, to give him the amount on the stipulated date of car delivery, then A would probably not have to borrow money from the bank and would directly take it from B, as and when he has the money. Since, there are so many A's and so many B's in this world, hence, in some sense banks are behaving as the brokers - finding the right mapping of A to B's. Thus even if people trust each other, we need a central bank for smooth cash flow between people who need it to people who have it.