I may be wrong, but most places feel the need to provide one or more groomed ways down the hill for the safety of all their guests. The factor that hasn't been mentioned is that 6 inches of powder also turns into countless bumps and moguls that are considered to be less than safe and desirable for newbie skiers and boarders. Grandma and the grandkids have to have a place to go or the entire family won't come.
As for getting stuck on greens in powder, there's runs at some of the hills I ride that I've never been able to carry enough speed to make without unstrapping.
Like I said. Just leave a few green/blues ungroomed, not the whole mountain. I've seen people get stuck on flat spots on groomed slopes. Depends on the hill. As long as it's not flat, you're golden and you'll move. 6 inches of powder takes a while to turn into moguls. As soon as it gets a bumpy mess....groom it.