What is the purpose of oil or butter in bread?
Breads get their structure from glutens--a type of protein formed by the combination of glutenin with gliadin.  Kneading and resting the dough helps the formation of glutens--I assume by shifting glutenin and gliadin molecules around, this increases the odds of bindings occurring.
Oils can bind to glutenin and gliadin and inhibit these reactions, so fats--oils and butter--definitely play a role in the texture control.
It prevents the dough from getting too elastic, which controls texture.  This elasticity change would also change the maximum air bubble size.  Altering resting times and yeast quantity also change these, but trading off for a different flavor.  Oil may play other roles, but these are what I recall reading about off the top of my head.  Yes, it does contribute to flavor as well.