Having rare-earth minerals is one thing, being able to extract and separate the rare-earth metals from their minerals is a completely different thing.

For now, China has a huge advantage in the facilities for the chemical processing of the rare-earth minerals, so that much of what is mined elsewhere still goes to China for the extraction and separation of the metals.

Some rare-earth metals are very cheap, like cerium and lanthanum. Even neodymium is not expensive. Unfortunately most applications also need at least small quantities of those rare-earth elements that are really rare, i.e. they form a very small fraction of the rare-earth elements contained in a mineral, and whose separation from the abundant rare-earth elements is also very expensive.

So this phrase that is too often repeated "Rare earths are not as rare as the name suggests" is actually false for most of the 14 REEs. Not rare are only lanthanum, cerium and neodymium, which cover only a small part of the applications of REEs, like deoxidizers in metallurgy and glass polishing and lighters. Most magnets with neodymium must also include other much less abundant rare-earth metals, to increase their upper limit for the working temperature.