Much of the solution that government was trying to provide during the Banking Crisis of the Great Depression was for a problem that government itself created. Emergency banking procedures were begun during the Republican administration of Herbert Hoover and enlarged by his successor, Democrat Franklin D Roosevelt.
States that had "unit banking" laws (where banks could have no more than one office, in an attempt to keep the larger banks from taking over) had far more desire to see federal "deposit insurance" laws put into place. Those states with "branch banking" laws successfully successfully resisted the siren call for greater government control--until 1933.
Ninety percent of banks that failed during the Great Depression were "unit" banks. By contrast, Canada had no unit banking laws, and did not lose a single bank during that time period.
"Adverse selection" involves the reality that those who have the highest risks are those who want insurance the most. This was the impetus behind Federal Deposit Insurance, a part of the Glass Stegall Act of 1933, the only significant legislation passed during the first 100 days of FDR's administration, and one that FDR actually did not support.
Banks continued to fail after Glass Steagall was passed, but serious bank panics seemed to have become a thing of the past. A major effect of the new FDIC (Federal Deposit Insurance Corporation) was that taxpayers were now on the hook for risk of bank failure and not the depositors themselves.
Glass Steagall also had the effect of requiring investment banks to be separated from commercial banks. Due to this requirement, JP Morgan spun off the bank called Morgan Stanley. The hearings for Glass Steagall were very tightly controlled, and later on it was found out that only a very few examples had been given where investment bankers used their inside knowledge to profit from the commercial side of their businesses. One of the highest profile cases, involving National City Bank president Charles Mitchell, was a clear case of nothing more than tax avoidance, which was already illegal. Furthermore, there was no evidence given that underwriting investment securities posed any extra danger to depositors' accounts.
Some of the most active lobbyists for Glass Steagall were the Investment Company Institute and the Securities industry Association, who represented groups who would profit greatly to no longer have to have commercial banks as competitors.
Before Glass Steagall was enacted, some investment-only banks existed. Research by the American Economic Review found that investment-only banks were more likely to have defaults than "universal banks" in the period just before Glass Steagall.