> If banks freely set rates as players in a competitive market based on prevailing inflation rates, demand for money, etc, that would be the "market rate" of money.

But, they do.

Of course, "inflation rate" is in large part a product of monetary policy.

> Now it very well may be that zero would be the market rate of money, and the Fed is doing a great job of estimating it.

The Fed sets interest rate targets, and then directly takes action which affect those things which you suggest should be the inputs by which the market sets rates, which the market then actually takes as inputs, and sets the actual interest rates that are levied in practice.

> But to say the notion of artificial rates has no meaning is a little odd.

The notion of artificial rates has no meaning, because the things you suggest should be inputs in "natural" rates are not products of nature, but themselves "artificial" in that they are in many ways influenced by policy, and the first of them is not merely substantially influenced by monetary policy, its one of the two main things (alongside, but usually ahead of, employment) that monetary policy is aimed at controlling.

And, as a consequence, what you describe as the mechanism for "market rates" as opposed to "artificial rates" is the predominant way by which central bank interest rate targets are achieved.