Focus on Bank Liabilities, Not Bank Assets
Back in 1993, in my discussant's comments on an Akerlof-Romer article on the savings and loan crisis, I made a similar argument. Here is an excerpt of what I then wrote:
Traditional banks are peculiar institutions. Traditional banks have depositors who want short-term, liquid, riskless assets. Yet these deposits are backed by long-term, illiquid, risky loans. This incongruity is fundamental. As we have seen, it cannot be easily fixed by a government policy such as deposit insurance.
There is, however, a simple, market-based solution: mutual funds. Individuals who want truly riskless assets can invest in mutual funds that hold only Treasury bills. Those who are willing to undertake greater risk can invest in mutual funds that hold privately issued CDs, bonds, or equities. Long-term, illiquid loans could be made by finance companies, which would raise funds by issuing equity and bonds. In the world I am describing, all household assets would be perfectly liquid. Preventing bank runs---he original motivation for deposit insurance--would be unnecessary, because changes in demand for various assets would be reflected in market prices.
In essence, the system we have now is one in which finance companies are themselves financed with demand deposits. Yet these finance companies hold assets--long-term bank loans--that are risky and illiquid, much in the same way that fixed capital is risky and liquid. Imagine that the auto industry financed itself with demand deposits. Undoubtedly, self-fulfilling "runs" on GM and Ford would be common, and the auto industry would be highly unstable. Indeed, the auto industry would probably be a major source of macroeconomic instability. The best solution, of course, would not be deposit insurance and regulation of the auto industry, but a change in the way the industry financed itself.