Kevin Drum says no:
If you're going to create some kind of system risk regulator at all –
about which I'm sort of agnostic in the first place – you want to give
the authority to an agency that's institutionally dedicated to reducing
risk and considers it a primary task. That ain't the Fed. It's just
going to get buried in the bureaucracy and forgotten there.
Assuming we are going to do it, I think it has to be the Fed, whether we like it or not. It's the Fed who is the fireman with the awesome power to print money, move markets, lend to the banking system on a large scale, and now even conduct fiscal policy, all without Congressional approval. Our textbooks speak of the Fed as a lender of last resort but very often it is the lender of first resort too.
If you stuck another agency into that mix, it would end up waiting for the Fed's go-ahead, once an actual crisis arrived.
OK, so the systemic regulator is the Fed. But then you can't make the systemic regulator too accountable to Congress without eliminating the quasi-independence of the central bank. There's not any comfortable point on the power-accountability continuum, mostly because we don't trust Congress to run monetary policy.
The stinger on the tail is this: we want the Fed to deliver low inflation. That means we let it be influenced by financial creditor interest groups but not so much by populist interest groups (Adam Posen had a good piece on this but I cannot recall the reference). Right now a lot of people are asking for more populist regulation without realizing that also requires more populist monetary policy.
It's very hard to get financial regulation right. It's the populist stuff that Obama wants to strip into a separate agency (for consumer protection) but it is difficult for such an agency to cover the major elements of systemic risk.