Would there be so many ineffective tutorials and bad analogies if having to use monads really wasn't a problem?
Unfortunately, most programmers trying to learn Haskell have not taken any abstract algebra courses, so these definitions and laws are deemed insufficient. Regular people want to know the exact nature of a thing — not just a list of mathematical properties that hold — and so they insist that there must be something more. But there’s nothing there!
EDIT: Apologies, I missed the subtle point this post was making!
I think chongli is actually in agreement with you
:)