What are the reasons to throw pizza dough beyond putting on a good show?
Related: How to throw a pizza dough?
Those who favor throwing pizza argue that it is the best way to stretch and shape the dough without risking a puncture or tear. Some claim this extra exposure to the air helps the dough retain moisture, while drying the surface. This improves the crust. ...and of course, there is the show. On the other hand, simply shaping dough on a floured surface appears to be fairly common and also results in a correctly shaped Neapolitan-style pizza.
A lot of it depends on the type of pizza you make. Where I worked we did thin crust pizza, and these were the reasons we tossed:
Speed. Trying to roll or pat out a 17 inch pizza would be very time consuming.
Consistency. Was easier to make the crust a consistent size and shape.
Space. Rolling or patting a person needs the table space 100% of the time. When tossing you can step back from the table and let another person get in to prep (or finish) their toss.
Job marketing. People wanted to work there just to learn how to toss, and it helped maintain that "authentic" vibe.
And as you pointed out, the show aspect of it. Kids loved to watch our staff toss.