This is a very well written post and I have a great deal of respect for its author. I also happen to find Category Theory to be extremely beautiful, but its beauty (much as the beauty of many other theories in physics and mathematics) does not rest upon its applicability to programming.
The ultimate answer to the question is more nuanced: understanding functors and monads is probably only moderately correlated with programming skill and not just in an enterprise software context (would it be of any use to an embedded programmer or a kernel hacker?). Additionally, using and applying a limited subset of category theory in practical context (lifting, functors, monads) does not really require understanding category theory per-se, although I'd imagine it's a good "gateway drug" (learning Haskell had this effect on me).
The ultimate answer to the question is more nuanced: understanding functors and monads is probably only moderately correlated with programming skill and not just in an enterprise software context (would it be of any use to an embedded programmer or a kernel hacker?). Additionally, using and applying a limited subset of category theory in practical context (lifting, functors, monads) does not really require understanding category theory per-se, although I'd imagine it's a good "gateway drug" (learning Haskell had this effect on me).