Fats play three major roles in cake baking.
First, they tenderize by coating the flour proteins impeding the formation of gluten.
Second, they aerate by catching air bubbles that augment the later action of the baking powder or soda which create bubbles in response to chemical reactions as well as heat.
Third, they trap and carry as well as enhance existing flavors.
The difference between solid and liquid fat, shortening or butter as compared to an oil, is that oil has little ability to trap air and so doesn’t contribute to leavning.
The result of forgetting to add oil to a cake recipe that calls for it is to miss out on some moisture and flavor, and endure a denser cake. How much this detracts is usually a matter of taste, especially in the case of a cake recipe already calling for eggs and sugar, the latter also a moistening agent because water-attracting ingredient.
I base this rant on my own experience and on watching well intentioned young girls attempt to develop fatless cooking techniques on their own (including ruining my cookware). In the end, healthy eating is more about the quantity you consume rather than about stuffing yourself with tasteless, nasty and badly cooked foods on the pretext that they’re without fat.
Fat in pan-frying accomplishes several essential tasks. While reading this list, imagine in your mind placing a filet, a vegetable or something else in your pan without an oil.
Fats for pan-frying include: