This is wildly shortsighted view of mathematics. Historically many of the subfields of math which are presently most valuable were considered useless for decades or centuries. Number theory, non-Euclidean geometry, group theory, and Boolean algebra, to name a few.
This is false dichotomy. Many mathematical achievements were produced while looking at practical problems: Fourier is a good one. For every mathematician that accidentally made a practical contribution, there are many more that produced nothing of value, and would have with a better tuned reward function.