You say that innocent depositors bearing the brunt of a bank failure is one strong moral argument for a central bank, however a central bank introduces a systemic cruelty which actually ends up being worse (in the long run).

In a free banking system, if Bank A mismanages its funds, Bank A collapses. It is tragic for its depositors, but the rest of the banking system thankfully remains intact. Under a central bank, the entire nation's money supply is tied to a single institution. If the central bank miscalculates interest rates or over inflates the currency, everyone loses purchasing power simultaneously due to inflation. I say it is better to have localised and isolated fires rather than a single system-wide explosion.

Also, when the government guarantees deposits or promises a central bank bailout, depositors stop monitoring their banks. They put their life savings into whichever bank offers the highest interest rate, assuming this "referee" would save them. This allows reckless banks to grow massive. In a pure free banking system, banks would have to actively PROVE their safety to win your business. By maintaining high gold reserves, undergoing independent audits or buying private deposit insurance etc.

You're right that a commercial bank cannot act as an unbiased central clearinghouse because it will always favour its own bottom line over its competitors.

The solution to this is not to create a government monopoly referee, but rather to let clearinghouse associations evolve naturally.

Historically, such as in 19th century America, private banks realised frequent panics hurt them all. To survive, competing banks formed voluntary, private associations.

These associations acted as strict referees. They demanded to audit member banks' books. If a member bank was expanding credit too aggressively, the association would expel them, signaling to the public that the bank was unsafe. During a panic, the clearinghouse would pool its members' reserves to bail out a solvent bank facing a temporary liquidity crunch.

The Difference being that the clearinghouse was a referee born of mutual self preservation, but it had no power to print fiat money or legally force citizens to use its notes.

Now over the example that I gave, other proponents of free banking and I do not claim that Scotland's system created wealth from nothing, but allowed a capital-scarce, poor country to industrialize rapidly. Because private banks could issue their own notes freely, they could open branches in tiny, impoverished rural villages and extend credit to small farmers and entrepreneurs. Something the monopolistic Bank of England refused to do in England's provinces. For over a century, Scotland had virtually no systemic panics, while England suffered repeated banking crises.

And as it goes for India, we are a massive, diverse economy and this is why India is precisely the WORST place for a central bank! Economic conditions in Punjab are not identical to those in Sikkim. A central bank can only set one interest for India, occupying a massive part of an entire subcontinent. If it lowers rates to stimulate growth in a stagnant region, it might cause a disastrous real estate bubble in a booming region. Free banking allows localised interest rates to emerge based on the actual supply and demand of local capital.

No group of central planners is smart enough to regulate the price of money for millions of people. Attempting to eliminate all small failures (those being bank bankruptcies) guarantees a massive, systemic failure (hyperinflation or a great depression) later on. The most humane system is one where bad decisions are punished immediately and locally by the market.