In a free market it would be more difficult for the banks to increase the money supply

General prices are not altered by the level of bank reserves. Cash reserves could be destroyed but still prices would remain the same, due presumably to the existence of deposit insurance.

Normally, we might expect prices to fall if reserves are (known to be) insufficient because the market will price for this loss, those holding cash will have extra value. People trust that the bank deposits will remain valuable to the government, or at least they do not concern themselves with the benefits of physical cash in a scenario involving the failure of the banking system, they don’t care about the solvency of the banking system. The level of a bank’s reserves would be more important to customers in a free market, (without deposit insurance) Frb would be more difficult.