Neural networks performance on a problem is a benchmark of its real difficulty. It gives us insight, a new perspective.
In millennia of deliberations what have philosophers have discovered about the nature of intelligence? And then .. a neural net beats us at all board games, another can solve differential equations, another can translate, another can see, and so on. Have we really not learned anything by these inventions?
Another advantage of DL is that it frames the problem of intelligence in mathematical concepts and rigorous evaluation.
I, for one, have reconsidered all my spiritual beliefs after learning about the agent-environment-reward model of reinforcement learning. A new way of framing the agent and life, so parsimonious and powerful. And it does not require a soul, or a god, or anything outside out real environment, and yet can explain so much.
The whole machine learning paradigm is another powerful concept through which we can understand how we might function. Previously you might wonder how emotion, thought, sensation, imagination and will relate to each other. Now we can understand how they might be implemented and wired together, and what principles support their function.