An individual bank would clearly prefer that the depositor maintain all of his or her funds at that bank, and would prefer to eliminate the need for depositor diversification by being able to offer higher deposit insurance coverage. Nonetheless, the depositor appears to have no great difficulty--should he or she want insured deposits--in finding multiple sources of fully insured accounts.
In addition, the singular characteristic of postwar household financial asset holdings has been the increasing diversity of portfolio choices. The share of household financial assets in bank deposits has been declining steadily since World War II as households have taken advantage of innovative attractive financial instruments with market rates of return.