The purpose of central banking is to protect private banks from bank runs. Free banking operated prior to the introduction of central banking and it was less stable. In free banking a bank either had the capital to pay its depositors or it didn't, and if it didn't it failed. Although this was a less stable situation it meant that credit couldn't expand indefinitely because each time one of the periodic bank failures occurred it would would reduce the money supply.
Another way to prevent credit expanding indefinitely would be to eliminate fractional reserve lending. But that wouldn't work out well for governments who often borrowed from banks to finance wars and other actions that were not supported by their citizens.
Another way to prevent credit expanding indefinitely would be to eliminate fractional reserve lending. But that wouldn't work out well for governments who often borrowed from banks to finance wars and other actions that were not supported by their citizens.