The easiest way to judge if a dough has been sufficiently mixed is by appearance. A properly mixed dough should have a smooth, satiny appearance. Mixing beyond what is required to give it this appearance is just extra wear and tear on your mixer. If the dough is under mixed, the result can be excessive tearing when opening the dough up into pizza skins.
Excessive mixing, on the other hand, typically results in the finished pizza having a more bread-like crumb structure rather than the desirable, open, coarse, almost English muffin-like crumb structure (which leads to a crispier finished crust). The two exceptions to this rule are for those doughs used for making frozen dough balls or frozen pizza crusts, and for those doughs that are used in a bake-to-rise application.
In both of these instances, the dough will not receive sufficient post mixing fermentation to give the dough any level of bio-chemical gluten development, and since the dough needs this gluten development for structure, such as in supporting the weight of the toppings, the mixer is the only place where it can receive the needed gluten development. Hence, longer mixing times are needed with these specific applications. And yes, the cell structure does close up and become more bread like in these applications.