Except they didn't corner the market, aside from when they're willing to sell them cheaper than anyone else. E.g. the company that
Fortune article focused on, Molycorp, stumbled in various ways and for various reasons, including lower prices because the PRC's initial restrictive actions were of course followed by counteractions, including recycling.
On the company's web site, they say they're putting their US facility in maintenance mode, ready to resume if market conditions warrant it, and are fulfilling customer demand from the PRC and Estonia.
So, no, in terms of rare earths they aren't a necessary part of our military and industrial supply chains. A trade embargo between us would hurt us both, and it would be devastating if they could interdict shipments from Taiwan, Japan and South Korea (one of the reasons we maintain an expensive military, although fab lines have to be exquisitely vulnerable), but otherwise at 0th approximation it's hard to distinguish your argument from those made just prior to The Great War AKA WWI.
I'd also note that if we even had a complete trade embargo between the US and USSR I don't remember/remember reading of it. In 1980 Reagan campaigned on lifting Carter's grotesque grain embargo to the USSR, one of many pinpricks he made after they invaded Afghanistan and mightily embarrassed him.