Unless you limit the travel of the shock you need to keep about 3 3/4" of clearance between the tire and fender. If you dont it will hit and can cause issues such as ruining your tire, pulling off the license plate and sucking it into the rear tire(if it's mounted on the back)and wiring like you said.
The stock fender blends in with all the trim lines on the bike and lines up with the seat, plastic inner fender stuff like that. If you wanted to drop it, I think you'd need a custom fender,and seat. Then you could cut off the factory rear end and make a set of nice metal fender supports weld them to the frame on the outside/inside of the rear fender. Outside would eliminate all the rubbing issues.