The 'chef' has paid his dues and is usually the one overseeing the kitchen and spot checks. He/she might have a signature dish that they don't want to share with others so they might prepare that personally. Otherwise its a staff that cooks your food or you'd be waiting forever.

But unless I want extra attention from other patrons who think I'm a snob, I will just tell the waiter the food was delicious, thank you. Also there are always guests who see in the movies and think they are big shots who ask the chef to visit their table. I chuckle when I hear the waiter tell them the chef appreciates the thanks but is tied up in the kitchen.