Export controls are one time use capability. Once you use it, other countries will develop alternatives, thus ending you leverage.
If China is using it, they know this is a temporary leverage and will go away within a few years. They need to get something tangible quickly while they still have the leverage.
unless they can produce elements from thin air, which requires being able to harvest supernova remnants or transmute elements atom by atom at a particle accelerator, they won't be able to develop alternatives with equal performance. They'll be permanently worse.
Rare earths are not just a technology. They're a material. It is much easier to control both the material and the tech needed to use it, than just the tech. The whole "rare earths aren't rare" thing? Not actually true. They are actually rare. Low concentration = rare.
The resulting atrophy of US industry for at least a decade is tangible enough
Decade? Try permanently.
You see this assumes WW2 and early Cold War competence from the US. Do you see that?
Do you see projects proceeding with great urgency, a bureaucracy with streamlined processes to quickly approve new projects and a population that's eager for change and improvement?
No, I see a population that is fundamentally tired, conservative and unwilling to budge even mentally, let alone physically.