Question on Rothbard's treatise on money.

Text is lifted from What Has Government Done To Our Money?

But if bank A and bank B are already having frequent clients between each other, then if $200,000 goes from A to B, and $250,000 goes from B to A, then only $50,000 or some significantly smaller amount need be redeemed by one of the banks. That could easily be way below the fractional reserves being kept by the bank. And it may well be the most that the bank may ever be called for in redemption.

Somehow I am not convinced that the increase in money supply caused by loaning of funds can easily be checked by the three parameters Rothbard described, and his hypothetical belief that the few educated people who understand the monetary expansionism of banks can stop it is hurt by the fact that in real life, even the few educated people who understand insolvency of public services or other schemes have failed to convince the common man against them. Is there any real life case of free society stopping monetary expansion of money substitutes?