This has nothing to do with the use of monads, but how they are explained. When your explain monads to people who don't no what monads are speach starts with "It is an arrow..." You are explaining monads to yourself, not to someone who doesn't understand monads (and consequently doesn't have a clue what arrows are.)
So far as I can tell monads are abstraction of state(though calling them abstractions of function application is more correct, calling it state is more intuitive to me, and how they are represented in the type system.) From there they get used for different things: Maybe == Nullable Types, List == lists, Either == Unions, St == Mutable State, IO == hide IO. Then a function that is pure and doesn't know about what your monad does gets invoked by the monad where the hidden state changes the flow of computation. Maybe performs a null check, List calls map, Either picks the type in the union then calls the function on that, St allows you to use and update the hidden state, IO performs IO then shares the result with you.
Now there is an explanation of a monad that doesn't assume you already know what a monad is. It may not be good since it basically says monads are sticky higher order functions masquerading as a data type, but there you have it.
Honestly, I'm tired of explaining monads in every HN article about Haskell. I've written detailed explanations for newbies 100s of times. If you want to learn more about something, Google it.
Remember, you understanding Haskell will improve your understanding of the Universe. You understanding Haskell will do nothing for me. So you can see how the incentives are aligned...
So far as I can tell monads are abstraction of state(though calling them abstractions of function application is more correct, calling it state is more intuitive to me, and how they are represented in the type system.) From there they get used for different things: Maybe == Nullable Types, List == lists, Either == Unions, St == Mutable State, IO == hide IO. Then a function that is pure and doesn't know about what your monad does gets invoked by the monad where the hidden state changes the flow of computation. Maybe performs a null check, List calls map, Either picks the type in the union then calls the function on that, St allows you to use and update the hidden state, IO performs IO then shares the result with you.
Now there is an explanation of a monad that doesn't assume you already know what a monad is. It may not be good since it basically says monads are sticky higher order functions masquerading as a data type, but there you have it.