Again, I agree that this was the ostensible purpose. But it only makes sense on the assumption that it is possible to control the economy in the first place; and that only makes sense on the assumption that economics is a precise enough science to be used for such control. I suppose it's possible that central bankers in 1913 actually believed that, but it seems highly unlikely to me. It seems far more probable to me that they knew they were essentially selling snake oil; but of course they weren't going to say so. They were tired of the government coming to them for money every time there was a financial panic, so they decided to do something about it, and if that meant selling snake oil packaged as "regulations and incentives to control the economy" to politicians who didn't know any better anyway, so be it.
> There's always winners and losers in any controlled situation
You're ignoring the alternative of a non-controlled situation, i.e., a free market that treats money just like any other commodity. There will still be winners and losers in such a situation, but it would be impossible to attribute that to the control preferentially advantaging some parties over others, since there would be no control to begin with.
Yes, you do. They borrow more money from the Fed, at the current Fed rate. This may not go through all the hoops a regular lendor requires, but it is a loan. That's why bank loan rates closely follow Fed rates. It's not money for free, it's very easy loans.
> No; but we are discussing "benefits of working at scale" that aren't really due to working at scale, but to special privileges that commercial banks have that private individuals don't.
Individuals also don't have to match the regulatory burden of the banks. Any individual could match those burdens (which may require a minimum loan amount, and a minimum amount of money on-hand) and try to get themselves certified as a bank, and then they could. They would need to meet the regulatory requirements too at that point though. You could argue that banks don't have enough regulatory hurdles in place to make up for the sweet deal they are getting from the Fed, but that's not the argument I've seen put forth.
> But when one looks at the history of how the Fed came into existence, it's hard to shake the feeling that it was the real purpose
Well, I don't see it that way, so it's it's not that hard for me. In order to try to control the economy, some regulations and incentives were put in place. Those are always able to be gamed, so you can either try to reduce the gaming to increasingly hard edge cases, or do away with the regulation. I think the regulation has a net positive effect, so I'm in favor of the former.
In other words, no matter what alternative you propose, if it was adopted it would be easy to look at it, look at the proponents that gained from it, and conclude the real purpose was to benefit those individuals. There's always winners and losers in any controlled situation, as the control always suits some better than others.