When China limited export of rare earths, leading to a dispute with Western countries, all that happened was suddenly Western mining firms became viable and attracted investment. China then dropped the export limits and dropped the price to force those companies out of business.
In some sense it's pretty obvious that a free market capitalist system will mostly lose in competition with a state regulated system, if the latter decides it is important to have control of a sector.
This is not really specific to state control -- it's a classic antitrust problem. A monopoly in one sector leverages it into control of another sector.
The problem being, what do you use for a remedy in this case? The US DoJ can't exactly break up the Chinese government.
That doesn't change the fact that I was right. There is basically no rare earth mining and refining in the US or anywhere in the Western world.
The refining capacity is all in China, and if China would stop allowing export it would absolutly cause an huge issue.
Adding mining and refinining capcity is a very significant challange.