Specialization is necessary to learn a field. But most innovation comes from the intersection of specialized knowledge with broader knowledge. Broad learning makes you more interesting and more creative.
New ideas frequently come from the cross-fertilisation of two separate fields. Francis Crick, who intuited the structure of DNA, was originally a physicist; he claimed this background gave him the confidence to solve problems that biologists thought were insoluble. Richard Feynman came up with his Nobel Prize-winning ideas about quantum electrodynamics by reflecting on a peculiar hobby of his — spinning a plate on his finger (he also played the bongos and was an expert safe-cracker). Percy Spencer, a radar expert, noticed that the radiation produced by microwaves melted a chocolate bar in his pocket and developed microwave ovens. And Hiram Maxim, the inventor of the modern machine gun, was inspired by a self-cocking mousetrap he had made in his teens.
Despite all this, there remains the melancholy joke about the scientist who outlines a whole new area of study only to dismiss it out of hand because it trespasses across too many field boundaries and would never get funding. Somehow, this is just as believable as any number of amazing breakthroughs inspired by the cross-fertilisation of disciplines.