These and other concerns are all quite legitimate, and his full essay is worth a read, as it cites other worries about the big regulation bill. The Fed is certainly not perfect. The moral hazard that may arise from its additional power is particularly troubling. But what was the alternative?
The too big to fail firms would not escape some new regulatory oversight -- that much was utterly clear during the financial reform battle. The new rulemaking they would face could either be undertaken by a new regulator or an existing one. The federal regulators other than the Fed are more subject to the direct whim of Congress and/or the President. For example, the Treasury might have had a new division of systemic risk instead. How would that have been better? At least the Fed is technically independent, though its leaders are appointed by the President and confirmed by Congress. When the political winds blow, it will surely sway less than other potential candidates for the job with stronger political ties.
That should be an important benefit to those who have views similar to Wallison -- that the financial crisis was mostly Washington's fault. He believes that government housing policy, which involved significant pressure from Congress and an implicit guarantee, is to blame. Isn't it at least a decent sort of compromise to have the Fed as the systemic risk regulator instead of an actual branch of the government or a less independent regulator that reports more directly to Congress or the President?
Simply not regulating wasn't a politically plausible option in Washington. Both sides of the aisle agreed that some changes in oversight of the financial market were necessary. Since Congress intended to provide some systemic risk regulation, how might it have done so more effectively than by bestowing incredible power on the Fed? The legislation could have instead made the Fed more of an observer of systemic risk, but without the rulemaking authority. Then, it could have required the Fed to submit any proposed rules or interventions to Congress for sign-off.
The problem with this, of course, is that when financial crises hit, they move very quickly. Congress does not. So allowing a new regulator the flexibility to act was likely important to some policymakers. But the tradeoff you face by providing that swiftness of action is precisely the worry that Wallison expresses: a world where bailouts are inevitable. So which is more preferable: more bailouts or deeper financial crises? It doesn't seem that they're both avoidable in a world where the future holds unpredictable risks.