The problem would be that if you wish them to look different, you will not be able to have different tile sets. The other thing that would happen is 2 of the sets would not be used. Also you would need 6 fields not 3. And finally there really is no advantage to doing it on 1 terrain that I can think of.
The thing you mentioned about choice, would actually make less because everyone would pretty much fight the same spot.
As far as having to rotate the terrains, we have settings that can do that automatically over a period of time.
HiTech