The problem with pre-heat or not depends on the thermal properties of the food.
Once upon a time I used to carry out physical tests at elevated temperatures on special materials. The oven supplier for the testing machine provided a handbook, which suggested one of three heating heating regimes depending on the thermal properties of the material being tested. Regrettably I can't now recall what the properties were, but the results fell into one of three categories that played the greatest part in heating the specimens (partly dependent on their dimensions): convection, radiation, or a combination of both. The idea was to ensure that the specimens equilibrated at the elevated temperature in the shortest time, due to degredation.
Cooking a pie is rather similar, the radiative effect might play a significant part on the food-heating process. However, radiant heat is dependent on the fourth power of the temperature, so essentially the maximum benefit will be gained when the oven has reached the cooking temperature recommended for that product, with not much contribution up to that point. So putting a pie in a cold oven and turning on, might result in much less radiative flux reaching the food, and so the product could be undercooked.
For an oven that reaches temperature in a very few minutes this might not matter much for a product that takes say 10 times that interval to cook properly, but 15 minutes in an oven that takes 5 minutes to heat could make a significant difference.