Why? Governments (read politicians) have an incentive to grow the money supply very quickly for short term gains at the expense of longer term inflation. Without the independence it is generally the case that
By Scott Beaulier and William Mounts in the WSJ: Obama Should Reaffirm Fed Independence - WSJ.com:
"While understanding the Great Depression is crucial, there is another event in America's monetary history that must be remembered: The 'Accord' of 1951. In this case, Mr. Bernanke should aim to repeat the past.and later
The accord struck between the Fed and the Treasury in March 1951 fundamentally changed the relationship between the two bodies that had developed during World War II."
"Without a firm commitment by the Obama administration to maintain central-bank independence at all costs, the Fed may become subordinate to the Treasury as it institutes the president's expansive plans to inject government into the economy. If this is the case (to paraphrase Milton Friedman) fiscal deficits will always and everywhere mean inflation."
It should also be noted however that Summers also later wrote that there seemed to be less relationship between Central Bank independence and unemployment rates and other real economic data.