That's what I was thinking too. While that's not Haskell 98, I believe it can be justified on Haskell 98 grounds by approximate equivalence with the representation of a foldable container by a binary tree. I'm no expert, but I think the hypothetical alternative formulation might look like this:

--Free magma
data Tree a = Leaf a | Bin (Tree a) (Tree a) deriving (Functor, Foldable)

--Adjoin an identity and a phantom.
--The phantom isn't Haskell 98, but
--it would be possible to accomplish the
--same purpose in Haskell 98
data R (f :: * -> *) a = Empty | FM (Tree a) deriving (Functor, Foldable)

--Improper, but probably sane for the purpose
instance Monoid (R f a) where
  mempty = Empty
  mappend Empty ys = ys
  mappend xs Empty = xs
  mappend (FM xs) (FM ys) = FM (Bin xs ys)

rep :: Foldable f => f a -> R f a
rep = foldMap (FM . Leaf)

We can apply rep to a foldable container to get a reusable representation of that container for folding purposes that is also a Functor.