There are certain styles of pizza doughs that tend to favor one kind of flour over another. For example, the flour that is most often used by pizza operators to make NY style doughs is high-gluten flour. There are several brands of such flours, including the King Arthur Sir Lancelot flour you referenced in your post. High-gluten flour is a strong flour and results in a chewy, almost leathery crust with a fair amount of flavor and dough coloration and the capability to handle a fair amount and number of toppings. By contrast, Neapolitan style pizza doughs, which have their origins in the Naples region of Italy, tend to favor the use of 00 flour, an Italian flour milled from national grains and sometimes grains from other countries. 00 flours are softer than the high-gluten flours and yield a softer, lighter, light-colored crust, which is usually sparsely and lightly dressed with toppings. As you have correctly noted, 00 flours are lower in protein (and gluten) than most other flours, and they are milled differently than our domestic flours, giving them characteristics that differentiate them from the high-gluten flours.. Sometimes, high-gluten flour and 00 flour can be combined to make doughs that have characteristics of both the NY and Neapolitan styles of doughs. The well known DiFara's pizzeria in Brooklyn uses such a combination in a highly effective way.
There are no hard and fast or absolute rules about the use of flours in different dough recipes. It is possible, for example, to use high-gluten flour to make a Neapolitan style pizza dough (as do many of the so-called "elite" pizzerias in NYC), or to use combinations of domestic flours, such as bread flour, all-purpose flour, cake flour and pastry flour, to come up with flour combinations that are similar to the 00 flour. It would be highly unusual to see a 00 flour used to make a classic NY style dough or a deep-dish dough, although I'm sure that someone somewhere has tried. As you get greater exposure to dough recipes and study them you will in due course find the best path to the pizzas that will provide you with the greatest satisfaction. Reading the posts at this forum will also be a big help.