I know that you have long been interested in the differences between pizza dough and bread dough so I wanted to be sure I understood your premise before replying.
I think the short answer is that a pizza dough can use more than one rise but that there are commercial considerations that benefit from only a single rise.
As you noted, most bread dough recipes call for more than one rise. Unless you are making a very wet dough, such as a ciabatta dough or a comparable artisan dough with very high hydration levels, there will usually be a couple of very pronounced rises of the dough. The first one is usually right after mixing and is the “fermentation” rise, which typically occurs at room temperature and during which time the dough increases significantly in volume (usually a double). Typically the dough is then punched down to expel old gases and to introduce new starch to the yeast, shaped into a ball or other form, maybe subjected to a brief intermediate rise, and then retarded for a relatively long period in the refrigerator to give the dough enough time to develop the fermentation byproducts that contribute to crust flavor, aroma and texture. The retarded dough is then subjected to a second significant rise at room temperature, called the “proofing” rise, before finalizing for baking. If desired, an autolyse or similar rest period, like a riposo, can also be used in the initial mix of the dough or later.
A similar process can be used to make a pizza dough. In fact, that is essentially what Bill/SFNM does with his Neapolitan and other doughs. After mixing/kneading his dough (for a brief period), it is subjected to a 20 minute riposo and then allowed to ferment in bulk at room temperature for about 8 hours. The dough is then subjected to a bulk retardation in the refrigerator for about 36 hours, following which the dough is divided, scaled and shaped into individual dough balls. The dough balls are then allowed to “proof” and rise a second time, for about 4-5 hours, and then formed into skins for baking. I don’t think that there is anyone who would say that Bill’s pizza crusts don’t have superb oven spring or a wonderful crumb structure. Obviously, the dough has enough gases and yeast at the time of baking, along with a very high oven temperature, to produce the exemplary results that Bill achieves. It also helps that Bill doesn’t overknead his dough. By contrast, most bread doughs depend on a long mix/knead time to develop the gluten structure. Bill’s gluten development is largely biochemical.
I personally think that the “single” rise that is common with pizza doughs is to a great degree to accommodate current practices within the industry for creating dough ball inventory and managing that inventory. Using small amounts of yeast and cold fermentation allows dough balls to be formed and put into dough boxes or proofing dough pans and to cold ferment without fear that the dough balls will rise too fast. Absent significant expansion of the dough balls, there is no need to punch them down or reshape them, which would otherwise be difficult to do with hundreds of dough balls and require an additional labor input and proper timing. In most cases, a cold fermented dough will rise a bit on the bench in preparation for shaping but it is usually not a long or significant rise (although the dough will usually hold for a few hours thereafter). At this point, it would not be wise in any event to reshape or reknead the dough, especially in a commercial environment, because of the potential for making the dough too elastic to work with in the normal time frame.
Even if the initial dough is fermented in bulk, similar to what Bill does, either at room temperature or in the cooler, or a combination of both, it is easy in a commercial environment to divide and scale the dough into individual dough pieces for subsequent use without having to subject the dough balls to another rise. The dough pieces can be shaped by hand but just as often the dough pieces are just run through sheeters or presses and put on screens, disks or into pans. If a skin requires proofing, as with certain pan and deep-dish pizzas, the skin is allowed to proof at room temperature or in a proofing box with humidity.
I suspect that there are ways of introducing multiple rise times in pizza dough, or more pronounced rises, but there is no particular need to do so in a commercial environment. We may do it as artisan pizza makers, as does Bill, but our motivations are different than most commercial pizza operators.