[Haskell-cafe] A question about mfix

What's wrong about giving mfix the following general definition?

mfix :: (a -> m a) -> m a mfix f = (mfix f) >>= f

I know it diverges if (>>=) is strict on the first argument. My question is, is this definition correct for all lazy monads? The documentation (http://haskell.org/ghc/docs/latest/html/libraries/base/ Control-Monad-Fix.html#v%3Amfix) says "mfix f executes the action f only once, with the eventual output fed back as the input.". So my definition looks like a valid one, doesn't it? I haven't fully wrapped my head around this monadic fixed-point thing yet. So, if you can give an example showing how my definition differs from a standard monad, that'll be great.