Normally, a monad transformer to provide a random number generator would be of the form StateT g, where g is a RandomGen. But I've seen some libraries (like QuickCheck) define their RandomT as:

newtype RandomT g m a = RandomT { runRandomT :: g -> m a }

with their monadic bind operation defined as

(RandomT m) >>= f = RandomT $ \g -> let (ga, gb) = split g in m ga >>= (\a -> runRandomT (f a) gb)

and return and fail as in ReaderT.

Can someone describe the advantages and disadvantages of doing RandomT this way? I mean, if your generator has a subpar split operation (and most do), this will obviously exacerbate any problems with it. Does it give any comparable advantages?