Oil in the dough facilitates handling with any kind of flour, it also promotes color and flavor, both of which are diminished with shorter fermentation times. As operators cut down the fermentation time of their dough, they added more yeast, sugar and oil to replace some of what was lost from natural fermentation. I don't believe they actually knew that though. I think the new formula evolved out of necessity for changing methodology and product specifications: ie uniform crusts for slice pies in a hurry.
If you look at Neapolitan pizza and the Lombardi formula, there isn't much difference; they are both flour water yeast and salt--but within those 4 little ingredients lies a vast difference in product and technique. The flours are different, the hydration levels are different and the oven is different. Neapolitan pizza is the mother recipe, but the Lombardi formula was the first American pizza archetype.
New York slice pies, New Haven Pizza and most of the pizza produced in the early part of the 20th century evolved away from the Neapolitan pizza Napoletana model. Even in Italy itself, after WW2, Neapolitans migrated to the rest of the country and brought with them their style of pizza and the pizzeria. However, in Italy, most Neapolitan style pizza is not true to the authentic VPN--but it is closer than American pizza ever was. To get the real deal, one must go to Naples.
There's really a whole clan of New York Style Pizzas--with different variations. This will be the basis of an article someday. So when I talk about NY style pizza, there are most definitely more than one type.