The goal makes sense in principle, but achieving independence is hard. Congress created the Fed, so Congress can influence the Fed:
With the Federal Reserve under more intense attack than at any time in decades, Ben S. Bernanke, the professorial chairman of the central bank, was schooled last month in how to handle the increased political demands of his job.
For months, he had warned — without anyone on Capitol Hill appearing to listen — that a seemingly innocuous bill to let Congress “audit” the Fed would gravely threaten the central bank’s independence.
It was alarming enough that the bill’s author was Representative Ron Paul, the quixotic Texas Republican whose new book, “End the Fed,” had just landed on the best-seller lists. Despite vigorous protests by Mr. Bernanke, nearly 300 House lawmakers and 30 senators had endorsed Mr. Paul’s bill.
But when he sat down shortly after 8 a.m. on Oct. 1 at the Rayburn House Office Building for coffee and muffins with Representative Barney Frank, the rumpled and wisecracking chairman of the House Financial Services Committee, he took in some blunt advice. Voters had become suspicious and unnerved by the Fed because of its trillion-dollar efforts to bail out the financial system, Mr. Frank warned. If the Fed really wanted to survive the disgruntlement in both parties, he continued, Mr. Bernanke would have to step back and let him devise a compromise.
That is, Congress cannot commit itself not to interfere, so the Fed will frequently react to the threat of interference. True independence is unlikely.
A different question is whether independence is desirable. If you believe the Fed does only good things, then yes, but that is unlikely. That is why Ron Paul, correctly in my view, argues for eliminating the Fed.