As long as we are politicizing the Federal Reserve and shredding its independence, why not Bill Clinton for Fed chairman? It’s not as loopy an idea as you might think. While the Fed chief has typically been an economist or banker, that’s not always true of central bankers in other countries. The former head of Iceland’s central bank, David Oddsson, previously served as that nation’s prime minister.

The thing is, when you look at the outlines of the Obama administration’s plan to revamp the U.S. financial regulatory system, a career politician as Fed chairman begins to kinda-sorta make sense. (Although Oddsson did turn out to be a bust.) According to an op-ed by White House economist Lawrence Summers and Treasury Secretary Timothy Geithner that generally described the plan, America’s central bank would grow in power and responsibility as it morphs into a systemic risk regulator. In addition to its continued monetary policy role, the SuperFed would supervise large and interconnected firms whose failure could threaten the stability of the financial system. (Why juice up the Fed? Since the central bank serves as a lender of last resort for the financial system, the government argues, why not give the power to help prevent problems for happening in the first place? That makes sense only if one overlooks the Fed’s so-so record as a regulator. One guess about who was supposed to be keeping tabs on Citigroup.)

Regulation by its very nature is a political act, balancing competing interests and claims from various stakeholders. (As it is, the Fed’s enlarged role during the financial crisis has drawn such lawmaker scrutiny that it is hiring its own lobbyist.) And how might those concerns mesh with the Fed’s role as an inflation fighter? The Fed already has a dual mandate — price stability and full employment — that some hawks argue serves as a policy distraction. A broader regulatory portfolio would further muck up the Fed’s mission. In another crisis, Regulator Fed might be tempted to argue for forbearance, so Monetary Fed wouldn’t have to resort to quantitative easing.

Charles Calomiris of Columbia Business School has pointed out, for example, that during the 1980s emerging market debt crisis many regulators loosened capital standards because they feared the macroeconomic impact of so many banks going bust. And what if a situation arises where what’s good for price stability is bad for the financial system?

Moreover, the White House plan would put in place a “council of regulators” to deal with systemic risk. How exactly the Fed would interact with that group is unknown, but it’s hardly a stretch to think a politician’s skill set would be helpful. And whose people skills are better than America’s 42nd president? Of course, a better choice would be to get the Fed out of the financial supervision game altogether and let it focus on monetary policy. Unfortunately, the Obama White House has gone out of its way to avoid political turf battles that would arise from a radical regulatory overhaul, which is why it is proposing so little consolidation of existing regulatory agencies. In fact, it might even be adding a new one in the form of a financial products safety commission.

There does look to be some good in the regulatory plan, particularly a push to make the originators of securitized loans keep some skin in the game. And it seems likely that at least the Office of Thrift Supervision is going to get the axe. Good ideas both. But while there may be a case for a financial regulator with systemic oversight, a SuperFed is not the answer.