What are the advantages of using a stove instead of an oven?
You are relying on very different forms of heat. Conduction vs Convection vs Radiation


Heat transfer, and the first law of thermodynamics
Principles of Cooking
Basic Cooking Methods


What happens when you heat something? A number of things.


Proteins Coagulate
Starches Gelatinize
Sugars Caramelize
Water Evaporates
Fats Melt


Depending on how you cook it, you're going to get different forms of each of those at different rates. On a stove, you can avoid too much moisture and fat from leaving your food by cooking it extremely quickly (in a stir-fry). . You can't sear something in an oven and you can't roast something on the stove. The two are simply not the same, because fundamentally the two are not the same, you are not going to get the same results. It's really as simple as that. You can't take two entirely methods and argue that you get the same results.