Your question made me think of Richard Feynman. He had this approach where he had a dozen difficult problems in the back of his mind and every time he learned a

Your question made me think of Richard Feynman. He had this approach where he had a dozen difficult problems in the back of his mind and every time he learned a new technique or perspective, he would re-evaluate each of them and see if the new technique could help get him closer to a solution. This made him sometimes come up with brilliant solutions that nobody else had thought of. So there can be enormous value in using insight from one domain in another domain. Point being, don't discount the value of using your brain in different ways - there's plenty of people hammering at problems from the obvious direction, and you're actually more likely to be able to contribute in a significant way if you're not a one-trick pony. Plus, by going with the grain of how your brain works, and what motivates you, rather than against it, you are able to be "productive" (actively thinking and learning) much longer and more effectively than by forcing yourself to work on something because you "should".