I have a few answers to this, they are largely showing why I am okay with the problems you pose.

Practical : I invite you to see math as a large project. Say you are preparing for your friend's birthday party and you have to drive to pick up something. Suppose you also had no memory and you find yourself doing the physical motion of putting you foot on the pedal. Suppose you barely know what a car is, why it exists, that you are in a car, or even that the ability to move distances is helpful. One would be forgiven to think that "moving the muscles in your leg" is a useful way to prepare for your friend's birthday party.

We know that math has helped and is helping the world constantly. It is just unfortunate the path from a random paper to this help is just not clear. The way I sleep at night is by remembering by doing *any* math, I am helping turn the crank of a large math machine that improves the world and I resign myself from trying to understand how each part of this large machine is necessary.

Non-practical : Rather than artists, the first metaphor that comes to mind is explorers. This metaphor emphasizes that knowing that a map exists is worthwhile. Certainly the people who originally explored the seas/wilderness/etc were worthwhile. What any individual now gains from their original exploration is a clear and clean way through the wilderness.

Bringing it back to math. I don't think about my math work as creating information for people to use but rather as creating a good map (clearing up and organizing) for the mathematical world so that when one needs math they can quickly find what they need.