Listening to music can help us focus and work harder. Poetic experiences let us appreciate life and understand people around us. Some things give practical utility and some aesthetic value. Neither is more important than the other. We have to eat to survive, but that is only the bare minimum.

I definitely appreciate things more that provide valuable utility or some other derivative value. You're right that some works are appreciated beyond their utility, for how they are experienced.

I do think there may be utility in these things even when the pattern is more apparent than the application. A good poem makes us feel something. I just wouldn't get the same feeling from a math problem unless it solved something for me. Not to diminish your appreciation for this, just that I find a poem more accessible.