There's always more to say, but I covered a similar question in this post. The major thing I want to add is that the Amorites, Kassites, Chaldaeans, etc were assimilated because they moved from somewhere else to southern Mesopotamia. There was no Amorite empire based in an Amorite homeland. The Persians, as with several Elamite and Assyrian dynasties before them, conquered southern Mesopotamia and ruled it (in part) from their own homeland.