The moment they start doing this, other countries will restart their mines and the Chinese leverage (and profits) will evaporate. Rare earth minerals aren't that rare.
Found the estimate in the report the Pentagon gave to Congress on this issue in 2013. Your proposed action would take the US, alone, 15 years (https://imgur.com/olWM3Xi).
I believe there's a few Australian mining companies with plans ready to go if China ever does this. The prices will go up, a lot, but the spice will flow.
From what I understand, it's not the mines that are the problem. In fact, China imports most of its rare earth materials. What they control is the refinement of these materials turning them from a raw form to something useable. I believe the US is finally starting to do something about this imbalance, but I'm unsure if its scale is great enough to have an effect. A refinement plant just came online in Colorado (or is it Texas?) in the last few months. I believe there might be more in the pipeline including Mountain Pass (in addition to the mine itself) in California. From what I understand, traditionally refinement is an extremely dirty process and as a result extremely costly to run especially with all the environmental restrictions and potential fines.
edit: latrare brings up another very important point. The patents surrounding the processes to refine RE materials. Take a look at who owns most of them...
I recall that China owns most of the latest patents on rare earth refinements. This should be obvious considering they are the most active in its refinement process.
Now, the irony is that if American companies want to start rare earth refining, then they must pay China for the use of those refinement patents.
Oh the irony.
Unless some American senator want to invalidate all of China’s patents on grounds of National Security. Oh the hypocrisy.
China has been maintaining a majority share of production for at least a decade at this point. I would wager that while that your proposed response is short as a phrase, actually getting production to match the currently relied-upon volume without China would take years, and I don't think stockpiles would last that long.
The US accounts for a small part of the global REM consumption. Even with their majority share, unless China is willing to burn the rest of the world, the US would be able to make do. And that's not even getting into transhipping which was used to circumvent previous REM export bans.
I saw it explained like this. Rare minerals are everywhere but they're spread out, and China's advantage is they will destroy a lot of environment to extract them while other countries are regulating protections for the environment. If that is true it would be very difficult for other countries to fill the demand?
I thought lots of existing mines had ore containing them, but can't make a profit extracting them, so they don't. How quickly such extraction/refining steps could be added, I don't know. (Am far from an expert though!)
Report: https://fas.org/sgp/crs/natsec/R41744.pdf