Boy, made me think on this one! Memories from my culinary school lessons came to mind but I had to go back to my reference books so that I could be sure I was giving you correct info
-- you are right in that certain cakes use fats and the creaming method to incorporate air into the batter but these only assist in the leavening process, cakes also depend on other ingredients, such as chemical leaveners, eggs, etc. for their height and texture.
here's a couple blurbs from my book "How Baking Works" by Paula Figoni that my be helpful
Chapter 10: Fats, Oil, and Emulsifiers:
Assists in Leavening: ..."In summary, the three main ways that fats contribute to leavening in baked goods are as follows:
- through the incorporation of air during the creaming of plastic fats
- by the air and water already present in certain plastic fats
- through the assistance of emulsifiers in high-ratio shortenings
Oil is 100 percent fat....Oil is the only common lipid that does not contribute to leavening in baked goods....Oil is used in quick breads, muffins and chiffon cake for a distinctively moist and tender yet dense course crumb."
So basically, a true cake uses fats, but cakes using oil (that are not a chiffon cake) are really more of a quick bread which is why they tend to be denser and have a different texture. These type of cakes depend solely on the other ingredients for their leavening.
Hope this helps.