Wood was hard to come by. Much of the area around Rome had been deforested (the Romans deforested many parts of their favorite colony, Spain, using wood either for firewood or for making charcoal for their BBQs). But at a certain point, you run out of easily available wood, and then cooking over fire becomes something the poor can’t afford. Hence, it was always normal and cheaper to buy already cooked food or to prepare your own and take it to a communal oven for cooking. This was even true in mediaeval Europe.
The Romans were good at “reusing” heat, though; the communal bakery ovens had water tanks on top, and the water heated by the baking process was then redirected through pipes to fill the baths. They also used it for radiant heating under their floors.
And the olive wood is oily and doesn't burn well like hardwoods, of which they had very few.
I remember walking through the ruins of Pompeii and seeing a corner store -- it had a long counter of wood with round holes in it, into which huge terra cotta pots would be suspended, full of soups or stews for sale for the day.
Also, even to today, women in the countryside bake or buy bread that has been cooked in the village brick oven on Monday to last the week. It is the origin of the crusty Italian loaf, since the crust helped preserve a soft interior.