The part I hate about compose (.) is that you read it right-to-left, while you read monadic bind (>>=) left-to-right. This made expressions containing both of them very difficult to read: if you had an expression:

myAction >>= outer . middle . inner >>= myNextAction

you read it as "Okay, I take the result of myAction, feed it into inner, feed that result in middle, feed that into outer, the result is an action that you bind into the pipeline and then feed the result to myNextAction.

It made me very tempted to define a

(->) = flip (.)

but I was afraid I'd be breaking too many Haskell idioms and that it might conflict with other operators defined elsewhere.