You can generally keep the kids in line better at an Applebee's than when you actually have to watch the food. (Yes, I know Applebee's isn't a real fancy restaurant, but it's the sort of place most people think of when they think of dining out somewhere nice). And the real competitor to cooking is often pizza delivery or a drive-thru, not dine-in.

IMO, the reason for that is that the meals you want to show off are usually the fancy foodie sort. To pick my most food-photo-friendly friend as an example, she posts things like "My take on wing night: grilled tare duck wings and sesame snap peas and carrot sticks" and "Chili lime chicken lettuce wraps and black bean cheddar quesadillas. #dinner" on a regular basis. One, kids don't know what most of that is, but will still tell you that it must be gross with a certainty that could not be shaken with nuclear weaponry. Two, they tend to prefer eating the same things over and over, which makes your photos really boring. Three, preparing food yourself is more time consuming than preparing it from a box, so lots of parents get out the Kraft Dinner and hot dogs, or the like, and that is again not worth posting photos of. Four, if you do try to get ambitious, usually the kids are involved in the cooking, which makes it more likely to be sloppy, and which is likely enough of a distraction that you don't want to be bothered getting out the camera. (And when you do, you're not showing off the food, you're showing off the kid)