Nicki does want to be Kim.
She wants to be global (those TPP foreign dates were a little bit tragic), she wants to be accepted by white people (soooo soooo badly, to the point where it hurts), she wants to be a successful businesswoman, she wants to be controversial (Kim showing her ass landed her on all the big lists, Nicki showing her ass landed her.... ?)
She essentially wants to be a mix between Lil Kim and Kimmy K.