Commercial banks prior to the 1930s commonly issued assessable stock to their directors and officers -- a form of stock that allowed the corporation to levy the stockholder for additional funds. The liability of the shareholder was therefore not limited to their investment in the shares. With the passage of Glass-Steagall, which established the FDIC, this form of organization fell out of favor as it was assumed that commercial banks were safe and it was no longer needed.

Investment banks continued to be run as unlimited liability partnerships until the 1980s. The partners were personally responsible for all debts incurred by the bank, and unsurprisingly, the banks were very conservatively run. Goldman Sachs, one of the most conservative firms, retained this structure until 1999. What changed was that the NYSE altered its rules to allow public companies to be member firms, and the investment banks decided to go public, converting to C-corps and listing their shares on the stock exchanges. The side effect of these two changes was that the investment banks began engaging in riskier behavior, which almost certainly contributed to the financial crisis of 2008. Post-crisis, the introduction of clawbacks has partially returned the concept of personal liability.

Unlimited liability is not needed or desirable for corporations in general, because market forces can lead to desirable outcomes in an efficient market. However, there's an argument to be made that personal liability could play a role in systemically important institutions, because systemic risk is an externality or market failure which cannot be solved by market forces.