Interesting discussion, let me throw in a different angle:
About two years ago I tried an experiment. I sometimes just open a small can of Hunts tomato sauce to use as pizza sauce (sometimes with some sauteed garlic/olive oil in it) and simmer it a bit not to cook it, but to thicken it up. This time I simmered half the can, and kept the other half untouched. I dressed a pizza, half of it with the uncooked sauce and the other half with the thickened sauce (I marked the perimeter of the crust with toothpicks).
After cooking and slicing, I didn't notice a taste difference between the two sides. What I DID notice, however, was that the mozz on top slid right off the "uncooked" side, and generally stayed in place on the thickened side!
I'll always go for seeded, sliced fresh tomatoes when I can, but here in Utard that's only 3 months or so. Cooking the "canned tomato sauce" a little bit probably didn't change it as it is already cooked a bit, but it was an interesting experiment nonetheless.
I toyed with the idea of putting fresh crushed tomato into a bowl, and then inserting an aquarium bubbler. This would (eventually) thicken the sauce via dehydration without cooking it at all, but I haven't gone this far yet.