"Technical complexities, partnership strains and pollution concerns are hampering companies' ability to wrest market share away from China"
This is a main reason China has a large market share in the first place. There are a number of rare earth deposits around the world but clean extraction and refining is expensive. China has been willing to go the cheap and dirty route. So everyone let china sell it to the rest of the world cheaper than local deposits could be exploited due to environmental regulations.
There are only three options:
Buy from China. Which may no longer be possible.
Local extraction but more expensive. With supply issues as production ramps up.
Local extraction but the environmental regulations get tossed aside due to National Security. Still likely to be more expensive than china and slow to scale, plus the added joy of pollution.