Given the laws of Monad that state apply = ap as well as the laws of Alternative that state
empty <*> f = empty, we can practically derive the MonadZero law empty >>= f = empty.
Thus, it seems to me that we do not need to specify this law in addition to the laws already present.

Furthermore, MonadPlus has the requirement that >>= distribute over <|>. Though as it extends Alternative which already requires distribution of <*> over <|> and again, since <*> = ap we already get that property. Am I missing something here?