It will be a very long time before mining the seabed for rare earth minerals will be anywhere near as economically viable (or even environmentally-friendly) as traditional mining.
It is just that everyone has relied on China for so long for this dirty (literal sense) industry that they are now effectively being held hostage. It is not due to the fact that "rare earth minerals" are actually rare and for a large part of the 20th century, the US, for example, was one of the primary producers and exporters.