Prompted by a question a friend asked me, I began wondering - why do we use ovens to cook food, instead of say simply relying on a hob, or a barbecue? By the way, I'm not suggesting that this would be a good idea, I do a lot of cooking in the oven, but from a theoretical viewpoint, I'm interested to know: what are the advantages that an oven has over other ways of heating food. What kind of dishes can best/only be made with an oven?
As you observe in your comment above, an oven directs heat at food from all directions, rather than just from the bottom. Some chemical reactions can occur only once you've reached a certain temperature, most notably browning reactions. You wouldn't be able to produce a crisp chicken skin or a crusty loaf of bread on the stovetop.
You can try to fake it with a "Dutch oven", which uses a thick pot to try to distribute heat from a stovetop to the sides. But it tends to trap humidity near the food, which can make things soggy, and still can't get the sides warm enough. (Dutch ovens were originally used in fire, where you could heap coals on the sides and top. You can't do that on a stovetop.)
Modern ovens have thermostats, something a stovetop lacks. That makes them very good for long, slow cooking, such as braising. You can do it on the stovetop, but with less control. Some ovens even have timers that will automatically start cooking at a specific time, and shut off based on time or temperature. That control also makes ovens good for keeping batches of pancakes warm, so that you can serve them all at once.
Finally, most ovens have broilers, which expose food directly to the heat from the top. You can't do that on a stovetop, since the heat on the bottom is diffused by a pan. A barbecue grill can produce a similar sear on meats, but broilers are necessary put a quick browning on meringue-topped pies.
Adjunct to the good answer above: An oven, especially a still oven, also has very little rapid heat transfer capacity. Which can be a good thing - things that resist heating, due to energy being used up to evaporate moisture or cause other phase changes or endothermic reactions, will not be FORCED to heat up to temperature - compare something held still in a 500°F oven for ten minutes (probably crisp) vs anything held still on a 500°F pan for ten minutes (probably on fire)...
At the same time, the same slow heat transfer also means that the food cannot seriously COOL the cooking medium (air) - a temperature gradient will cause convection (not forced convection, as you have in a convection oven!) and thus air movement that will replace cool air with hot air...