Indeed, that's interesting. For example, for oil, the US has an annual cost of $0.2b for storing about $44b worth of oil i.e. a 0.45% annual cost. You'd expect if the reserves are dumped for an entire year for example, that smart investors would be happy to start paying a 0.45% annual cost once the price drops by slightly more than that. At 5-10% at such a scale, despite other price fluctuation risks, that's already a significant arbitrage opportunity that would generate enough buying power to put a floor under a small price drop.
That having been said, the US actually ran a planned long-term programme for oil storage. But if someone suddenly floods a market, there probably isn't infrastructure and expertise to immediately seize that as an arbitrage opportunity. If it happened every few years then there'd be tons of cheap storage, if it happens once every few decades, then sudden gluts probably dump the price with little capacity for investors to immediately buy back in. And this is coincidentally a few years short of derivatives taking off on a big scale, Allende died the year of the Black-Scholes model, which would've made everything more frictionless and easier to invest and trade in for the various parties (producers, investors, storage, buyers etc)
Of course it wasn't the only factor, it may have dropped prices by a few percent and that's already very significant. Remember that a lot of US employees and advisers left the country after the copper industry was appropriated, replaced by people with very different backgrounds and no experience to manage these companies. I've seen some sources that said the price of production went from 20 n something cents to 40 n something cents, while the price on the market was something like 49 cents. Profits were squeezed hard. Combined with sanctions on Chile (much of Chilean copper went to the US, Europe and Japan, big allies who could impose quotas and tariffs), a small price drop due to extra copper flooding the market and similar issues in other markets, could and indeed did create layoffs, economic woes and friction in Chilean society.