Who wants to heat up an oven to 450°F or higher on a hot summer day? If you use a grill to make pizza, you can keep the heat outside where it belongs.
This is the #1 reason I grill pizza. I love me some homemade pizza, I could eat it once a week, but in the summer I use my oven as little as possible. They're also dead on about grilling one side for 2 minutes first and flipping, that's the key. The first time I grilled pizza I didn't flip it...no good.