Let's take that further: you wouldn't want to use your code above either, because it would be impossible to tell why the parser failed. Which is going to be really frustrating once it fails. And if it doesn't fail the first version is fine.
import Data.Either.Combinators -- from the either package
strSum :: String -> Either String Int
strSum = fmap sum . sequence . fmap tryReadInt . words
where
tryReadInt w = maybeToRight ("not an integer " ++ w) (readMaybe w)
This keeps the bulk of the method the same. Being able to go e.g. from Maybe to Either with only few changes (as long as your code is sufficiently general) is one of the nice things you get from all the Haskell abstraction. You can't really do that if you start with exceptions (unless you're in IO).
