This continues from my comments here. Banks are already an oligopoly now, and they already try to control the price whatever way they can (but always around fed's determined rate). My focus on this point is not so much on how they want to price each individual loan, but how much more capital buffer they will be required to raise for each loan they make. When I say capital in this post, I mean bank equity. Banks are not reserve-constrained when they make loans, but they're capital-constrained.
Banks don't need to have the reserves/deposits firsthand when they make loans,but the central bank will want to see that they have adequate equity buffer for the loans they make. This means that at least 6% (the current standard) of their loans are backed by shareholder equity, and not 100% is funded by reserves/deposits. That implication is that if they make bad loans, there is an equity amount that will get the first haircut before depositors' funds are in danger. Central banks that enforce Basel standards want to see adequate capital in the banks. That Basel-mandated ratio is 6%, or lending at 15 times capital (equity). I'm suggesting that should be higher, so that even at zero fed rates, banks are not tempted to play the interest spread carry game.
My take on 'The natural rate is zero' is that when the Fed stands ready to lend banks any reserves they need, then then it is tantamount to saying they are practically zero rate. Any amount is available as necessary. My use of it in this post is that Fed discount is not what should determine cost of loans to the public (since the Fed manipulates it all the time, and cause a lot of distortions). What should determine cost is the level of risk. The riskier a loan a bank makes the more costly it should be. The most efficient way I think risk is costed is via the amount of equity capital a bank should set aside to back the loan.
Equity is not cheap. Shareholders will demand a higher return if they know a bank is being risky. Whereas fed rate can be made s cheap that it doesn't matter to banks whether they are extending risky loans (they know the Fed stands ready to bail them out). But if the banks stand to lose a lot of equity before the fed steps in, that's real cost, and determined by market sentiments, not the Fed's. If they have to raise more equity, their cost of capital gets higher the more risk they take. This is of course assuming shareholders are given the right assessment of the bank.
The fed keeps bailing out the banks because it is culpable in making them extend so many loans because of the low interest it charged them, while at the same time deregulating banks and enforcing a low capital environment. If the fed continues to throw money at banks and forces to make more loans than is prudent, then they will have to stand ready to bail them out again.