I agree with Tom- I think the “bulk method” is a remnant from long ago, before refrigeration was available (and cooling at different rates wasn’t a concern).
Tom touched on the temperature related proteolysis issue, but the bacteria and yeast also behave very differently at a lower temperature, producing flavor compounds at different rates (in addition to and partly because of the lower pH discussed in Tom’s post). A warmer temperature will produce more “alcohol” and “sour milk” flavors, while a lower temperature will produce a much richer and more complex flavor. When baked, the lower pH will also inhibit Maillard browning, which is what contributes the complex toasted flavor and aroma.
In other words, improperly cooling the dough will effect both the flavor of the dough itself and the flavor contributed by the bake.
The short answer is that weighing the dough balls to 19 ounces (for example) is much more precise and consistent than “grabbing a handful of dough”, and will give you much better control over your food cost and your bake. The smaller dough mass will also cool much quicker.
The rolling and cross-stacking that you mentioned are in aid of rapidly cooling the dough. Rolling the dough also helps to align the gluten network.
A quickly cooled dough will provide a better structure, a better flavor, better texture and crumb, better browning, and better workability.
Sorry for the long, rambling post- I didn’t have time to write a shorter one.