It's not clear to me that category theory, functional programming, what have you, provide insight into why things work. In fact, it seems like they might cut the opposite way -- moving from vicissitudes to simple abstractions.
Category theory provides the tools (a language, a set of theorems, etc) to understand why certain things are necessarily true, rather than just "true in practice" or true because of a happy coincidence, similar (IMO) to how complexity analysis gives you the tools to know that merge sort necessarily has a certain baseline performance, rather than just happening to run through all your unit tests quickly.
