I think the word 'rare' in rare earths here is merely implies expensive. That's why having cheap alternatives is such a big deal.
Interesting to note that there is quite big movement towards rare earth free electrical motors in the last few years that rely only on cheap, readily available materials. Some expect that to grab up to 30% of the market in about a decade. Similar technology is also being used for creating wind generators that don't depend on these expensive/rare materials.
No, 'rare' in this case means dilute. They were named this back at a time when there were few uses for the substances and they were generally considered worthless.
Interesting to note that there is quite big movement towards rare earth free electrical motors in the last few years that rely only on cheap, readily available materials. Some expect that to grab up to 30% of the market in about a decade. Similar technology is also being used for creating wind generators that don't depend on these expensive/rare materials.