Suppose we divide everyone in the society into two corporate A and corporate B, (or similar to an island with only 2 people), each year banks loan out 1 Billion to A and 1 Billion to B, and they do production and consumption and trade with each other. They need to return the loan plus interest. Since the money supply is only 2 Billion, where is that extra interest come from?
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As a result, the original observation might be more close to reality: Everyone's saving is depleted slowly by the banks, and saving becomes more and more difficult
Exactly! You have nailed the reason why the 2007/8 Credit Crisis has morphed into a sovereign debt crisis, which is morphing into a currency crisis, which will morph into a systemic collapse.
In a true capitalist model, loans are made and interest is due. The interest rate is the price of money which should be set by the market. Successful businesses/individuals pay back their loans and interest from profits, unsuccessful ones
default on their loans and interest which means a loss for lenders/banks. Debt write-off is the mechanism that money is transferred from banks back into the economy preventing all the money piling up in banks - because of interest. If the losses are too great then whole banks go bust, freeing up a lot of money back into the economy. The market will set higher interest rates to reflect higher default risk. This is a true capitalist model which is the environment for a successful world-beating economy.
The problem is that the whole system is FUBAR by government intervention!
The rot started after the 1907 recession in the US at a time when economic booms and busts were seen like a force of nature, uncontrolled. When government decided that it had to control the economy, by backstopping banks with printed money, the Federal Reserve was created. It was inspired by the Bank of England which had progressively taken control of the UK money supply. In 1920 this process was complete in the UK too.
Throughout the 20th century government intervention has grown and grown, the cradle to grave nanny-state which has created a massive entitlement dependency in all western economies. In hand with this bank failures are banned. So all banks get bailed out one way or another. This means that money has to be printed to maintain flows of interest. Interest rates, the vitally important price of money, being set by central banks is like having a crystal-meth addict at the wheel of your car. Capitalism has been broken by government intervention. Money supply has come increasingly from credit which monetizes future production giving the illusion of prosperity (because banks can't go bust they can lend irresponsibly to fog-a-mirror borrowers).
Excessive government debt leads to a sovereign debt crisis. Money printing leads to a currency crisis. It is all can-kicking which can go on for a long time. Think of someone falling from the top of the Empire State Building, As they pass the 3rd floor they can still report "All OK so far..."
Bitcoin can change all that. It can't be printed so bank lending in a bitcoin economy will have to follow true capitalist principles. Governments would be massively reined in, savers and producers will be rewarded for their hard work and frugality. Bad banks will go truly bust. Deflation will make everyone richer as prices keep falling. I suspect that income taxes will have to go in the trash-heap and that only sales taxes could be used for government income. The whole western economic system would hum along nicely.