It actually works very well with the economic cycle that way. When times are good, interest rates are bid up because there is more demand for borrowing. When times are bad, interest rates are bid down because people will save rather than spend. At some point, the low interest rates become attractive to businesses who will then borrow, invest and rehire to improve the business cycle again.
This is why, before creation of the Fed, we had panics and economic downturns lasting a couple of years or less before they were righted.
Once the Fed seized the role of setting interest rates, downturns can last much longer, sometimes more than a decade as was the case of FDR.
Do you have any numbers to back this up? I thought the downturns were less frequent and shorter, on average, after the Fed was created compared to before.