Considering that cheese is their most expensive ingredient by a large factor, I think they care a great deal. I've never met a pizza guy that wasn't acutely aware of the quantities of cheese he was using.
While we're on the topic of cheese, the water from the cheese seems pretty extreme in some of those shots. I'm sure that there's a strong cultural preference towards wetter pies in general, but, I have a hard time picturing a Neapolitan regular reaching for one of these pies if a pizza with Craig's cheese was next to it.
I'm wondering how much of it is a cultural preference or if it's, like the variations in leoparding, another aspect of high volume pizza making- that they just can't painstakingly drain the mozz like a home baker might do.
Definitely cultural. The soupy center is not a defect. It should not be thought of as a defect, consequence of production limitations. If you drain the cheese then you end up with a drier, more American pizza. But I guess I'm one American who does not prefer American pizza.
That soup in the middle where all the flavors come together is essential, IMO. After you finish the pizza you take the pizza bones and sop up the leftover pizza soup from your plate. It's awesome stuff.
If you think about the simple artesian process, a wet pie is just a natural consequence. You're suppose to lay down tomatoes you've just crushed, spread some basil you've just picked, hand tear some cheese you've just made, pinch of salt, swirl of olive oil. Bake it in 50 seconds. That's automatically going to give you a wet pie.