I used to feel this way too, so I'm not trying to be coy, but really that's a property of a (some) Functor(s), not a Monad (except in that all Monads are also Functors).

Monad is just the pattern where you combine Functors. Some Functors can be pattern matched upon to "escape" their values. Functors like IO cannot. IO would still be (academically) useful if not for its Monad instance... you'd just only be allowed a single effect in the entire program!