There are other sources of rare earths but capital is required to develop them.  Unless they are given an assurance of a market price adequate to service the debt they can't be developed. Likely only a sovereign govt. could provide such assurances, as the venture would be vulnerable to being sabotaged by the Chinese simply by selling rare earths at prices below the cost of production for the new mine. And a government guarantee would be labeled "Socialism!" We are hoist on the petard of our own economic ideology.

The USA could easily this problem by negotiating an agreement with China that either gets an agreement on the minimum prices at which China will sell rare earths or agreement to sell rare earths to the USA at the same price they are sold to Chinese companies and making access to the US export market contingent on that agreement. But that would be serving the national interest of the USA but not the corporate interests of the energy companies and the financial services companies involved in importing manufactured goods from China.

"It is not necessary to have hope in order to persevere."