In order to keep Bills in their portfolios, banks had to constantly buy new bills as the old ones matured into Gold coin. One hundred percent of Bills mature in not more than ninety days... so, in case of unusually large demand for Gold, the bank would simply cut down on Bill buying... and allow Gold to accumulate and meet the demand. Worst case, stop buying... or even go into the superbly liquid Bill market and sell (re-discount) some bills even before they mature. No runs on the bank!
If we only stick to the three legs, we have a stable, market driven financial system; the Classical Gold standard came close. My father used to refer to pre-WWI days, with a fond faraway look in his eyes as 'The Peaceable Days'. Under the Classical Gold Standard, the world enjoyed the most peaceful and prosperous era in Human history. Unfortunately, the camel had his Note... er nose... in the tent. Chicanery began on two fronts. https://www.a1mint.com/shop/