[pron]

> I say explicitly because I know there is a tendency to say that some given structure is a monad and we didn't realise it; but that still doesn't really prove that it is all that useful in the general sense

Exactly. That is what I call mathematical- vs. cognitive-abstraction. They are not the same thing, and in the case of programming languages, only the latter matters. A mathematical abstraction is simply the naming of a pattern; a cognitive abstraction is a human solving a problem by explicitly thinking of said pattern. The former is either true or false; the latter is either useful or not (and the utility is completely orthogonal to any mathematical considerations).

> I appreciate your explanation but again it fails to actually show it being useful outside of the context of working around Haskell's strict type system

I think it isn't useful as a cognitive abstraction (and the problem isn't Haskell's type system, but its purity from effects). I believe that monads as a cognitive abstraction are foreign and harmful to imperative languages, which have an equally-powerful cognitive abstraction -- the thread -- that fits much better with the rest of the language's abstractions and I think is much more useful for most people.