I am not a Strong AI guy. So I think AI does not and cannot "explain" what Chalmers' calls the "Hard Problem of Consciousness." (HPoC)

I also think HPoC is a more interesting problem than AI itself. So for me the top benefit is that thinking about the foundations of AI help you clear away the red herrings on the way to understanding HPoC.

Besides this top benefit, others include:

1. Stresses and helps us evolve our understanding of human intelligence. People don't often realize how closely psychometrics (IQ etc.) is related to AI. Lewis Terman created the modern IQ test. Stanford was also a pioneer in AI at that time. His son, Fred Terman is widely considered one of the founding fathers of Silicon Valley. Lots of other such separated-at-birth things.
2. Stresses our anthropomorphic conceits. Thinking about foundational AI issues has helped divorce our idea of humanness from such things as creativity, emotions, reason, humor.... all things that have been shown to be properties of certain kinds of computational phenomena (at least to my satisfaction). Hollywood still likes its terminally clueless, feel-good, pander-to-humanist tropes: "A machine can never replace the essential human ____________" (fill in your favorite idiotic human conceit dialogue)
3. Helps us understand the phenomenology of intelligence wherever it occurs. We now understand Darwinian evolution for instance, as a kind of global optimization and therefore "intelligence" of a sort. Ditto the heating and cooling of metals ("simulated annealing" is also a popular optimization technique). By divorcing the mathematical processes that underlie intelligence from the semantics that distinguish intelligence, we learn a lot.
4. Helps us understand anything in computational terms. You can view cities as self-organizing intelligences for example.
5. Helps frame and sometimes solve difficult metaphysics problems, or at least shed light on them: Searle's Chinese Room helped understand symbolic computation. The computational brain-in-a-vat thought experiment helps us understand mental models. You can get a lot of insight into free will. etc. etc.
6. Helps us understand the unnecessary elements of why we behave in certain ways and thereby understand humanness. AIs can solve Rubik's cube or beat humans at chess, but they don't attack those problems the same way humans do. They take advantage of their different resource constraints. Such research helps us understand that there is no right way to solve the Rubik's cube or play chess. There's merely the best human way, the best super-computer way etc.
7. Helps metacognition: attempting to create an intelligence in our own image effectively creates a mirror that we hold up to ourselves, a mirror that provides a better and better reflection every year.