Of course, I'd agree with CDNpielover on this. The recipe is the recipe. The amount of herbs and selection of herbs is optimized for tomato paste. Even if you used puree or crushed tomatoes or whatever, they are not processed in the manor of paste, so the entire flavor profile would be off.
I guess that's one of the biggest weaknesses of this forum (IMO), that a vast majority of recipes here are dough recipes only...with a few, "meh, I took some crushed tomatoes and sprinkled the pizza with oregano" so-called sauce recipes. The exception is in the deep dish recipes, which aren't really sauce, per se, but at least directions are given. (One of the inherent strengths in this forum, OTOH, is that it is truly a crust forum full of real *bakers*. This is a dough forum first. I acknowledge it and actually dig it...although I wish someone could clone Aurelio's sauce, but now my digression has a digression...)
Anyway, this is a complete recipe, from start to finish. If you don't have paste and the other ingredients, go with one of your tried and true sauce recipes you like. It just isn't Pizza Factory.