Paging the Dough Doctor!
This is a question made for Tom Lehmann.
I'll disagree about the deep dish lineage. DD was a style conceived long after other pizza was being made in Chicago. I will also disagree with the "Midwesterners are yokels" theory that Mad Ernie served up. Really, bro, there are 50M people in the Midwest. We're not all that dumb.
Nor is the Midwest some ingredient-less backwater, where we all sit around and pine for those New York ingredients that never make it west of the Hudson.
The real question is, what is the role of oil in dough? From my own experience, I would agree with jeffereynelson. Oil makes dough really easy to work with. This dough is sheeted in restaurants or rolled out at home. I.e., it isn't for tossing. So besides extensibility, oil also adds texture, affects crumb, etc. Again, forget the NY comparison. It's a completely different animal. The texture is much shorter, with less gluten and less chew. You want to aim for something that is crispy and crackery on the bottom and softer on top. There is also a LOT less dough per pizza. No "bones" to discard, either.