The point about rare earths is that they aren’t rare at all, they exist everywhere, just at very low concentrations. rhenium is in minerals found everywhere, just at concentrations of about 1 part per billion. The reason copper and molybdenum ores are used as a source is because they possess it in higher proportions, and the cost is reduced as it is byproduct.
Yes, the price will go up; yes, as the price goes up alternatives will be found; but it won’t run out, and in a cost product like a jet engine, there will always be a source.