The divine drink of nectar that emanated from the churning of the milk ocean is just like one more medicine. It has no power to take care of the resident of the body, the Atman. It only takes care of the body and protects it from becoming old and from decaying. Have you ever heard that the devas like Indra and others who drank that amRit have become Realised Souls?
Their only goal has been endless sensual enjoyment. At least for the human species, sensual enjoyment tires one out after some time since the body ages; so a human being has every chance of turning to something more permanent, something spiritual. The devas on the other hand have no way of learning by experience that sensual enjoyment is not the end of it all.