When duplicating a type of a nested family within a family, the parameter associations tied to any and all parameters within that type should also copy. Pretty straight forward I would think.
Also, you should be able to assign parameters to nested family parameters family wide. So there should be a right-click option of "Set parameter Associations" when right-clicking on the family. Wanna get really crazy? How about the same option when right-clicking a category within a family.
@kimberly_fuhrman-jones if this idea is the same as another, please combine. I tried searching because I figured someone had already come up with this idea, but couldn't find it.