By definition they are not, the name does not cover the cargo. They may appear less than other, lighter metals, but
Despite their name, weird-earth elements are – with the exception of the radioactive promethium – relatively plentiful in Earth’s crust with cerium being the 25th most abundant element at 68 parts per million, or more abundant than copper. They are not especially rare, but they tend to occur together in nature and are difficult to separate from one another. However, because of their geochemical properties, rare-earth elements are typically distributed as rare-earth minerals in economically exploitable ore deposits.
An important reason why China is such an important source is because it is rather environmentally damaging to mine these minerals. And mining is in any case labor-intensive, so economically it is soon more profitable in China with lower wages than in other countries.
In the US there are also stocks, but these mines are closed because they can not compete economically and there much local protest was against the environmental effects of mining.
Japan is in a somewhat more difficult situation. They do have a very large electronics industry, but no potential own sources. Frankly, I expect this stock to be used primarily as a political and negotiating tool, rather than actually going into exploitation. Much easier to ask for lower prices by threatening that you can “always start to mine your own minerals” than actually doing that investment.