i didn't realize the NY sauce had no oil in the sauce. But, really, I can't understand why a drizzle of EVOO isn't a must for pizza sauce, pre or post baked. To me, all tomato sauces could use EVOO (only, not pumice, not pure, etc) In fact, I can't remember one dish not utilizing some kind of fat in it...evoo or pork fat. I think its as important as basil as something to use with tomatoes. Just my opinion.
Nick, beyond the impact of the coal ovens, imo, you're looking at the greatest fundamental difference between New Haven and NY style pizza. When I first started researching New Haven pizza, I was in shock by how frequently oil was drizzled on the pie pre-bake. The coal places in NY add oil, but, when you get into archetypal deck oven NY slices, you rarely find it. They'll use vegetable oil in dough for it's baking properties, but you'll almost never find evoo on slices.
Fat is everything in food. Fresh mozz, unless it's bufala, gives off almost no fat. So, when pizza first made it's way to America, and fior di latte was all that was available, fat supplementation was critical. Since these were Italian immigrants, it only makes sense that they'd reach for the oil of their homeland, evoo. If we were having this conversation 100 years ago, then I'd wholeheartedly defend evoo in NY style pizza. But the melting pot kicked in and pizza evolved. 20th century aged motz, on a thin crust pie, gave off more than enough fat to please the taste buds, and notoriously cheap, margin watching pizzeria owners jumped at the chance to save a dime or two by omitting the evoo.
Was the result of this frugality a good thing? For people that love the taste of evoo, no. But the phenomenon happened, with sufficient market penetration to define the style. When you add evoo to NY style pizza, it changes the nature dramatically. It no longer tastes like NY style pizza. It's something else. For some, it might be better, but, for the city that defined it, for the millions that worship at it's altar, evoo is outside the canon.
Some people like evoo. Some like provolone. Others love sourdough. That's good for them. But none of these have any place in authentic NY style pizza.
When you say 'pizza has to have evoo' you're saying, 'I prefer NH to NY style pizza.' There's nothing wrong with that. Before you completely pass judgement, though, I would ask you to eventually try my NY style pie and see if you miss it