Where did you find the information that the doors are mids and the rears are subs? So you're saying it is a component system? I don't think so which is why I'm asking where you got that information. I was under the impression that the door and rear speakers are full range with whizzer cones (not even two way speakers) not separate components which would require separate amps.
Would a true sub woofer increase listening pleasure without overpowering the music? If set up correctly the answer is Yes, positively. Is it needed? That depends on individual taste. For me it was a necessity, for the next guy it's a waste of money. It all depends on how much into music you are.