why separate tanks for grey and black water?

When you are at a site with full hookups, and you have two tanks, you can leave the grey tank valve open and take long showers and not have to worry about filling the tank up. Also, most of us put chemicals in the black tank to control the smell. If you only had one tank and you were having to empty it every couple of days, you'll be putting chemicals back in every couple of days. I can go a week easy, probably longer, without having to dump the black tank.

If you only have one tank, you can't leave the valve open when you have full hookups, because you need to keep some water in the tank so you don't create a dried out mountain of human waste in the tank.