" Why spend time learning to play chess when I can write a program that will beat most humans? "
To develop thinking skills. Planning, changing, thinking many steps ahead.
Everything you learn from chess would make you a better computer programmer.
Also, I doubt you can right an algorithm that will beat most mediocre chess players. Try it some time.
Yes, you said most humans. If you literally meant most humans, well then duh. Most human don't know how to play.
"Even a novice programmer could create a very strong chess AI using information that's publicly available."
ah, you are a C&P programmer. Great. Like we need more of those.
"but it's largely a solved problem now, "
I don't think you know what that means, becasue it is not largely solved. Checkers is largely solved..
Of course what does largely solved mean? When speaking of an algorithm, either it's solved not or it's not.