In David Deutsch's book The Beginning of Infinity, he argues, that the purpose of science is not to merely predict or to model the world, but to explain it. And he gives in my opinion convincing arguments, why a better explanation is needed to advance science. Therefore, he deduces that pure empiricism has failed. Because no matter how much data you have gathered, an explanation does not follow from it. The explanation is always an insight the scientist has to contribute. Then it is open to scrutiny by criticism or experiments.
I guess he would argue the same is true for mathematicians. Merely constructing proofs to arrive at theorem, is of no intrinsic value, if it doesn't spark an idea of a more elegant formalism that corresponds to a simpler and even more far reaching explanation.
I cannot recommend this book highly enough to anyone who is intellectually curious, not only about epistemology.
That's not to say there isn't value in building mathematical insight for humans, just that there is a goldmine and a lot of people know what to do with gold, even if they don't understand the ecosystem surrounding the gold.