Tran,
Even staying within the boundaries of the NY style, there is a fairly large range of flours that can be used, from all-purpose flour to high-gluten flour. I discussed some of the historical evolution of the flours for the NY style at Reply 3 at
http://www.pizzamaking.com/forum/index.php/topic,7527.msg64720.html#msg64720. I would say that, today, high-gluten flour is perhaps the most common flour used by NY pizza operators who specialize in the New York style. But there are still NYC pizza operators still using all-purpose and bread flours for that style.
The use of 00 flours is not a matter of purism. It is also not a matter of high-protein flours being better than lower protein flours. If one wants to make an authentic Neapolitan pizza, the way to do it is to use a 00 flour and a very high temperature oven. That's it. 00 flours are made of grains that differ in protein content than those available in the U.S. Because of the protein/gluten make-up of the grains used to mill 00 flours, their rated absorption values will be lower than for the flours milled from U.S. grains, despite the finer grind of the 00 flours. You can see the different specs for a couple of the Caputo flours (Pizzeria and rosso) at Reply 17 at
http://www.pizzamaking.com/forum/index.php/topic,2951.msg25328.html#msg25328. You can compare those specs with the KASL flour in the same post. For specs on other King Arthur flours, see
http://www.kingarthurflour.com/professional/specifications-conventional-bakery-flour.html.
I have discussed some of the differences in using all-purpose flour, bread flour and high-gluten flour in Reply 2 at
http://www.pizzamaking.com/forum/index.php/topic,1994.msg17592/topicseen.html#msg17592 and also at Reply 2 at
http://www.pizzamaking.com/forum/index.php/topic,8654.msg74968/topicseen.html#msg74968.
In my experience and observations on the forum, and I have worked with many many members who wanted to make Neapolitan style pizzas using 00 doughs with their standard unmodified home ovens, most such members tended not to become converts. They might find ways of combining 00 flours and U.S. flours, usually high-gluten flours, but they eventually tend to lose interest is using only 00 flours. As I have mentioned before, the forum is littered with the bodies of members who have tried to make credible Neapolitan style pizzas in their home ovens. Bill/SFNM even commented on the smell at Reply 7 at
http://www.pizzamaking.com/forum/index.php/topic,9568.msg83003/topicseen.html#msg83003 
. My advice is not to try to relate the 00 flours with the other flours. Except for 00 blends with other flours as mentioned above, I would keep the 00 flours separate in your thinking and use.
Peter