The assembly originally came from a lap steel guitar and the cover was actually a pair of horseshoe pickups which also formed a wrist rest.
In the 70s the horseshoe pickup was replaced, but the surround was retained.
Rickenbacker teleased a subsequent model, the 4004, which had no surround, but customers kept buying the 4003.
So, the reason it is so big is because that is what customers want!