The most common reason given for the warm-up period is to prevent or minimize bubbling, which can occur in the finished crust if the dough is too cold when being shaped. The cutoff temperature above which this risk is reduced is about 50 degrees F, although I usually aim for around 60 degrees F. I have read that some pizza chains require that the dough be above 50 degrees F before using. But not all operators follow the rules. Some routinely use cold dough, especially if they are about to be slammed. Plus, they will dock the doughs--sometimes too aggressively--to reduce bubbling and, if necessary, use bubble poppers to deflate the bubbles that start to form in the crust. Some operators who shape the skins by hand also prefer to work with dough on the cool side because they find that it handles better. But that's not universal. Some operators find that a warm dough is easier to stretch and shape.
You didn't indicate where you worked, but some pizza operators intentionally try to achieve bubbling and blistering in their crusts. A lot of customers like the bubbles and blisters and, consequently, they are a differentiating factor for the pizza operator. They become a "signature" feature of their pizzas.
It's also useful to keep in mind that many cold fermented doughs, especially those that have been in the cooler for less than a day, will quite possibly have had little expansion because of the suppression of yeast activity while in the cooler. Allowing the dough balls to warm up, even if for only an hour or two or three, lets them expand and develop some gasses to produce a decent oven spring and a better texture. Of course, some skins are allowed to proof before using because of the type of pizza being made. Proofing is common, for example, with pan pizzas and some deep-dish pizzas and with Sicilian styles.