All wheat flour contains enough damaged starch to feed the yeast, so even though yeast feed on sugar, added sugar doesn't play much of a role in dough expansion, but, rather, it's predominantly added for flavor and browning.
Oil also promotes browning.
In order for gluten to form in dough, one type of wheat protein, glutenin, has to make contact with another type of wheat protein, gliadin. When you knead dough, these separate components rub against each other and gluten is formed. Gluten is the structure of bread. Too little and the bread will collapse, too much and it will be tough. Oil has a tendency to coat these two proteins and prevent them from making contact, which, in turn, prevents them from forming gluten. Because pizza dough is typically made with high protein flour, it produces chewy crusts. When you inhibit gluten formation by adding oil, it decreases elasticity and tenderizes the final product.
Just like I don't use sugar for yeast food, though, I don't use oil for tenderness- at least, not beyond a certain point (4% or less). If toughness is an issue, there are a few ways to decrease gluten development and create a more tender final product- all of which, imo are preferable to increasing oil, since increasing oil has the tendency to produce an oily tasting crust. Less kneading = less gluten, also lower protein flour = less gluten.