“Lithium, and cobalt are indeed considered to be rare earth...”
They aren’t actually very rare. There is more of both of them available for mining than common elements like lead and tin.
They are expensive because we haven’t needed them much until recently so a lot of new mines need to be created.
Which the BLM and the EPA will no let happen so here in the sates they are rare. No matter how many fish are in the water you can’t catch any if there is a no fishing sign. Makes fish from that pond pretty rare.