Fractional reserve is really what makes a bank a bank instead of a gold/dollar holding company. The problem for banks in not so much debt defaults by people who they loan money to, but lots of people the bank owns money to wanting it back all at the same time.

We could get rid of almost all the bank default risk by making banks match the maturity of their deposits with the maturity of the loans they make. But with less risk, the bank would not be as profitable most years.