Yes, they deal with Kleisli composition (which I intuitively think of as taking regular composition and "twisting" it with a monad) but that is different from w

Yes, they deal with Kleisli composition (which I intuitively think of as taking regular composition and "twisting" it with a monad) but that is different from what I meant. You can't take two different Kleisli arrows twisted with two different monads and combine them in an obvious way the same way you can compose/combine regular arrows. That is why all the tricks with transformers exist. You somehow have to get everything to be a monad again because Kleisli arrows can't cross monad boundaries.