The problem isn't with the mathematical concept of monads, it's that Monad is a typeclass in a hierarchy along with other totally abstract category theoric classes introduced at different stages and people use them with varying levels of knowledge and ignorance so things are placed arbitrarily and there are a bunch of ambiguities. Just look at this [0] mess. Is that really what we want?

[0] https://wiki.haskell.org/wikiupload/d/df/Typeclassopedia-dia...