Neither lithium nor cobalt are rare earths, and China isn’t particularly dominating their production either. The leading producers are other countries. These are completely unrelated to the rare earths problem.
With rare earths the situation is that China isn’t only leading in production of the ores, but also in processing capacity, and the technology needed for it. The US already is the second largest producer of rare earth ores, but they still have to send them to China for processing because they can’t do all of it in the US. For the same reason, China produces ~90% of the world’s permanent magnets (these use rare earths like neodymium or samarium). Basically it’s not about developing sources for the ores. Rare earths are not that rare in the first place. It’s about the technology and capacity to do anything with them.
I do agree that the impact might not last long. They’re just forcing the competition to work faster. But maybe the explanation is that they think that making everybody speed up their rare earths development doesn’t change much in the long run anyway, while throwing a wrench into the US industry right now is a pretty good deal.