People tend to denominate their contracts in the base currency. In the old system before the Fed, the value of this currency in the US would fluctuate as much as 50% in one year.
It is hard to imagine with what bizarro world economic actors is this an elegant and sound basis on which to conduct trade, that a bank could find that all of its customers suddenly find it 50% harder to pay off their loans, or conversely, that its capital stock is worth 67% (1/150%) of what it was before. Now imagine how that feels for the customers, or shareholders. Imagine a society when the money can come or go in floods and what this means for every contract, every wage, every price.
Why would you want this? So you can satisfy some Rothbardian itch about an "elegance" constraint that means very little in practice?
The Fed tends to target price levels. In addition to being a very elegant basis with which to conduct trade and form contracts (as Milton Friedman pointed out), stable price level targeting has the advantage of actually working out pretty well, unlike 'free market' currencies or fixed standards. NGDP targeting is probably better but that's outside the scope of this discussion...