Eric Posner makes a very common point:
If you have government-supplied insurance, then you have to have government regulation of people's financial activities. There is no way to avoid this conclusion. In a world without such regulation, banks would make excessively risk loans because they get the upside and the taxpayer bears the cost of the downside.
Indeed, I have made it myself. But I wonder if it is actually true.
Almost everything in the world has negative and/or positive externalities. But despite this, we do not intervene to subsidize everything with good negative externalities, or punish everything with bad. That's because things with substantial negative externalities often contain sufficient punishment to deter the individual; likewise, things with positive externalities often carry enough reward to produce a socially optimal amount. For example, if I am a bus driver, the negative externality of my suddenly jerking the steering wheel to the left and driving the bus off a cliff is much higher than the cost to me--many lives against my one. But my own life is very valuable to me. The threat of its loss is enough to deter such behavior 99.9999% of the time.
Bankers take risk in order to make money, and they control risk in order to avoid losses. But the losses they are most interested in are not to their shareholders. Rather, they are worried about the loss of their jobs. As long as the bank regulators fire any managers who put the bank in receivership, I can see no difference between an unregulated private system without deposit insurance, and a system with. That isn't to say that there is enough regulation in either situation. But if there is a problem, it is that bankers have a socially less-than-optimal risk appetite, or that the punishment for driving a bank into insolvency is insufficient. The moral hazard from deposit insurance doesn't much enter into it.
The moral hazard for depositors may be large. But I doubt it. Most depositors are not capable of determining whether a bank is faulty or sound, and they weren't in 1830, either.
The reason that desposit insurance requires tighter regulation is that the government wants to minimize the cost to itself--not society, for whom the losses would be the same whether the government or the bank paid them. I think this is wise, for many reasons. But not because of moral hazard.