This is incorrect. The gold standard was abolished in the US because it was too hard for the US to control macroeconomic policy [1] (especially import/export rates) through gold. The US already had elaborate ways to manage reserves to help in keeping the dollar steady. It was also a matter of dwindling gold reserves for the US.

Whatever your thoughts are about the gold standard, it was not instability that did it in.

[1]: https://www.wsj.com/articles/when-the-u-s-gave-up-gold-11625...