I’m sure someone will, the moment it becomes more economical than exploiting what we have on Earth (including recycling—it’s not like the rare earths are consumed, they’re just discarded because extracting the pristine stuff is still too cheap!) I’m not going to hold my breath.

Rare earth is everywhere, there just needs to be an economic incentive to mine them. Which is still low and you cannot get to an industrial scale in a few days.

Maybe after the price of rockets drops by several orders of magnitude and the price of obtaining the elements on Earth also increases by several orders of magnitude.