As home sales stall, there are 2 effects on the demand for mortgages - 1) the number of mortgage decrease and 2) size of the mortgages decrease (lower home prices). As a result, the overall dollars demanded should also decrease.

With lower demand for money, interest rates should drop until the point at which money becomes cheap enough to incent home buying.

Why then must the Fed control rates?

I assume that its because the Fed is already controlling rates. So if they keep the rates too high during a recession, then banks get squeezed until they stop lending. They need to lower rates to create a sufficient spread to incent banks to lend.

What if the fed didn't exist? What if it kept rates fixed at 0?% Would the market regulate itself sufficiently? Banks would presumably lend as much as they could at high rates. If the demand dropped, they would lower rates. What would the spread be? It would be whatever they would obtain equity at - so banks would be forced into long-term prediction of interest rates... which they do now - would they be better at predicting if there was more on the line?