As far as I know, the demarcation problem has not been solved which makes answering this question "correctly" impossible.

That being said, (modern) economics is typically referred to as as "social science" and operates how I expect most people expect a science to operate. Namely, formulating hypotheses and models, testing them using data, and throwing out the theories that turn out to be wrong.

The process is, of course, much messier than a physical science like chemistry or physics for many reasons. The largest is that it is unfeasible and/or unethical to run many controlled experiments that one might want to run.

The market does set the (long-run) price for money.

The price of money is the real interest rate which is the nominal interest rate (managed by the fed) minus inflation (determined by the market). If the fed tried to perpetually lower the nominal rate, this will lead to higher inflation (assuming nothing else is changing) as the market restores the "natural" real interest rate.

The reason we do this is because highly variable inflation in very costly. For example, it makes it risky to lend money (as you don't know if the money will be worth much less when you get paid back due to a large bout of inflation) which makes it costly for businesses to raise capital and depresses the economy.

By manipulating the nominal rate so that it "absorbs" all the market fluctuations in demand for money (which cause variation in the real rate), the fed is able to maintain a low, stable inflation level and eliminate this problem. This is why you will sometimes hear about the fed's "inflation target" and why we find it optimal to have an entity managing the money supply.