China has more rare earth deposits than the US but that's a bit misleading. Rare earths show up in trace amounts all over the world. China has them in higher concentrations.

The bigger issue is that China has been the main refiner of rare earths for decades. That means they have all the infrastructure for actually making it available and they've developed a bunch of technologies and processes to do it way cheaper and more efficiently than anyone else can.

I don't know the pricing specifics of EV motors but I have some familiarity with electric motors, in general. The technology hasn't really changed much in a long time. We've have 3 phase motors and hall effect sensors for ages. They're better than older electric motors but the huge technology leap, that made EVs practical, was the batteries.