Bernanke claims that interest on reserves is not a subsidy of banks.

Given the large stock of reserves that commercial banks now have as a result of QE, the Fed can no longer raise interest rates by keeping banks short of reserves. Or so Bernanke argues. As he puts it (I’ve put his words in green italics):
 
“In the past, the Fed achieved the desired level of the federal funds rate through market operations that affected the amount of bank reserves in the system. By making bank reserves more scarce, the Fed pushed up the price of reserves—the federal funds rate. By making reserves more plentiful, it pushed down the funds rate.

However, as a consequence of the large-scale asset purchases that the Fed undertook between 2008 and 2014 to help support the US recovery—purchases that were financed by the creation of bank reserves—the quantity of reserves in the system is now very large. Because banks are essentially satiated with reserves, modest changes in the supply of reserves will no longer have much influence on the federal funds rate. Rather than varying the supply of reserves, the Fed now manages the federal funds rate by changing the rate of interest it pays on reserves (as well as the interest rate it offers in so-called reverse repo transactions with money market funds and other private-sector institutions).”

Hasn’t he unwittingly admitted to a weakness in his own argument there? That is, as he rightly says, interest rates can be adjusted by adjusting the availability of reserves, or put another way, if the reserve requirement imposed on banks is adjusted, that will influence interest rates without there being any need to pay interest on reserves to commercial banks. E.g. if the amount of reserves that banks are required to hold is RAISED, will tend to raise interest rates. To that extent, there’s no need to pay interest on reserves to banks. Certainly that’s what China does.

Reserves / base money is essentially money issued by government or “the state”. Physical money ($100 bills, £10 notes, etc) are also a form of state issued money. Now if someone (or a bank) wants to build up a stock of that money and for the sake of argument, keep it under their mattress or lodge it at the central bank, then that’s their right. But there’s no good reason they should be REWARDED at the taxpayers’ expense for doing that.