Initiality comes with a powerful universal property which allows you to, internally, prove statements about the constructions you perform. If you give me an element of
data Nat = Z | S Nat, I can perform induction on it.
Polymorphism on the other hand requires you to appeal to external principles such as parametricity (*) to recover similar reasoning principles. If you give me a function of type
(a -> a) -> a -> a, I will know it is bound to be a natural number in disguise but will be powerless to exploit that fact.
Additionally in predicative systems with a tower of universes, initiality is typically size-respecting whereas an encoding via polymorphism will land you a definition that lives one level up in the hierarchy due to the universal quantification. If you want to iterate these constructions, that's bad news.
(*) caveat: there are type theories attempting to internalise parametricity