The Chinese are very adept at driving western rare earth mining operations out of business to eliminate competition. A good example of that is the now defunct Molycorp rare earth mine in Colorado. The Chinese drastically lowered the price of rare earths and drove Molycorp out of business, and then raised the price again. There is no way to beat them at that game unless we have state support for such ventures. Also the waste from these mines is normally radioactive so the pollution problem is very severe. The Chinese just bite the bullet and accept this, but here it would be problematic for us. Anyway, it would take many years to build up a production capacity to challenge the Chinese.
Rare earth metals per se may be a relatively small part of the trade balance, but they are extremely critical for our high-tech economy and this could be used to exert a great deal of leverage against us. If we were not able to build our military gear, and the necessary equipment to keep our economy going we would be in a world of hurt.
Or a tariff.