Question: I have moved into a house with a nice Wolf-range griddle, and I would like to know what the primary advantages of the griddle are over a cast-iron skillet, including, is there anything I can do with a griddle that can not be done with a skillet?

I have found that the primary downside to using the griddle is the time it takes to heat up, so when cooking for one, I would choose the skillet. The primary advantage of the griddle is that it provides a larger, easier cooking space. 

Am I missing other major advantages of having a griddle?

Answer: 
I would say the biggest advantage, which you've hinted at, is being able to use a spatula for quick and easy flipping (think pancakes, french toast, etc). Apart from its shape and size, there really is no other difference (even the difference in heat-up time, I've found, is negligible).
I'm going to just use to frying pans ('skillets'). The lack of sides allows stuff to fall off too easily - I fried chopped onions today - and there's no carrying handle - so you can't move the griddle to plate up. The other downer - my griddle's cast iron and it's just cracked while heating it !