This

newtype M m a = M (m a)
  deriving newtype
    Functor

produces something similar to

instance Functor m => Functor (M m) where
  fmap :: forall a a'. (a -> a') -> (M m a -> M m a')
  fmap = coerce (fmap @m @a @a')

but as wiki:Roles2 points out, this fails for methods such as join_:

class MonadJoin m where
  join_ :: m (m a) -> m a

newtype M m a = M (m a)
  deriving newtype
    MonadJoin 
 -- Couldn't match representation of type ‘m (M m a)’ with that of ‘m (m a)’

I think the user should be given the option to respect the roles or not by supplying unsafe wiki:Commentary/Compiler/DerivingStrategies

newtype M m a = M (m a)
  deriving unsafe newtype
    MonadJoin

-- -( Produces `unsafeCoerce' instead of `coerce' )-

-- instance MonadJoin m => MonadJoin (M m) where
--   join_ :: forall a. M m (M m a) -> M m a
--   join_ = unsafeCoerce (join_ @m @a)

This lets us (newtype-) derive a host of instances that we currently can not: Traversable, Distributive (currently forbidden due to distribute), Trace, ProfunctorMonad / ProfunctorComonad, ...

It does not seem like lenses (FunctorWithIndex, FoldableWithIndex, TraversableWithIndex) work with this though