Okay as a Chicagoan I'm inclined to say that squares are better for thin crust and Detroit style (which is a rectangle), and pie slices are better for Chicago style. The trash is for New York style. HOWEVER. This does appear to be the optional cut for thin and similar crusts for equal distribution of smaller pieces than a pie cut.
I have no idea how a directed air jet would work here. But I did fill my waterjet cutter with pizza sauce so fingers crossed I've found a less malodorous solution to geometric pizza.
Some people like the burnt laser cheese taste but I'm not into it. I prefer to use my laser to add grill lines to my burgers the way BK does to the whopper before microwaving it.