I think they dont do this because you would have to render the map twice which would have a huge impact in performance. Starting with bf1 the deploy screen is a realtime render where as with bf4 and previous titles it was just a map and not an actual render which allowed the devs to have a deploy view in the deploy screen. I could be wrong but thats what i believe it is.
Edit: Maybe they could make the rendering of the parrot camera with very low settings so it wouldnt have a huge impact in performance but who knows.