And yes we leave both greys open all the time but not the black.
I leave 'both' tanks closed all the time when parked with sewer hook up.
The gray tank needs water to 'move' things along too. Bits of food, water you cook foods in, dirty dish water,greasy plates when you wash them, etc will just stick to the bottom if you don't have any water in it like when you leave it open and go rancid if you don't leave the tank fill up with water.
I have been parked next to MH's in areas where they allow you to dump the gray on the ground. And it STINKS almost as bad a dumping your black tank. I will never stay at a place that allows discharging of gray water EVER EVER again it stunk so bad.