The Chinese killed foreign competition primarily through price dumping, not due to scarcity of ressources, esp for military applications (whose demand pales in comparison to the private sector). So asking the Chinese to lower their prices again is a bit hilarious, as it would again result in killing off renewed efforts to re-establish industries, that cost-cut themselves into oblivion 15 years ago. The issue with Chinese REE availability is not so much pricing but rather limiting overall production and reliable access for manufacturing industries, esp for Japan, as they are exposed more heavily to Chinese supply chains than everybody else. This is a problem caused by greed and ignorance, not scarcity. As it takes years to restart production in this industry, it creates the illusion of scarcity of REEs. While its of course nice for manufacturing to have new deposits with attractive yields, lack of deposits as such is not at all the issue and land-based efforts will have similar overall effect.
I wrote about rare earths a while ago and read as preparation the report from the German national agency for geology stuff as well as other sources.It's not as simple as you assert; some rare earths are not that widely available in known deposits in a satisfactory concentration.