I'll try to answer by explaining the principles and reason for mixing and what that process does - apart that is from the simple combining of the ingredients.

It is possible to over work the pizza dough and one of the outcomes of it is, is to make more of a close texture sponge sort of bread. The most important objective of mixing and later folding is the formation and development of gluten. You do need to stretch the gluten which means longer than just cleaning the bowl. 4 to 5 minutes wouldn't over stretch at a medium mixer setting. I mix now for around double that - say 10 minutes - partly because I use wet mix and longer mixing stretches the gluten further and allows me to handle it. If you stop just as the bowl is cleared the gluten would be insufficiently formed and is also a cause of stopping you from stretching the dough and also difficult for you to fold and shape. So 4 to 5 minutes at medium I'd say is a minimum. Arguably with pizza dough you can allow longer mixing because you need the extra gluten in order to stretch the dough to a thin base compared with making loaves. To over simplify, the thinner the base, the more stretched gluten you need. You cannot stretch and make a thin base with insufficient gluten.

The key thing is envelope folding after the first rise and before shaping preferably between a few rests. This further stretches gluten but also is responsible for those nicely elongated holes in the dough. Then "balling", and flattening by hand stretching and never by rolling pin or flattening of any sort as you will be killing all those lovely baby air bubbles you worked so hard to create. Never trust anyone who uses a rolling pin to make the base for they know not what they do, unless that is if you are after a sponge like base.

Hope that helps.