Square cut is even a Domino’s option online. That’s not just a Chicago thing is it?
Detroit pizza, at least, is always square cut and also from square pans. Even here in Squarecutopolis, deep dish and stuffed is always pie-wedge slices.
The dominant local pizza maker here in the northern mid plains city I live in serves their pizza (round, fairly thick but not pan crust) cut in the squares. They refer to it as a ‘party cut’. If you request it on ordering, they are happy to cut it in wedges.
The other pizza places, especially the national franchise ones, cut it into wedges.
The square cut for round pies is definitely something that is more prevalent in the Midwest. I’ve seen it in St. Louis, Wisconsin, Indiana, parts of Ohio, and probably in Michigan, though I can’t remember for sure. I’m not counting Detroit pizza (or the myriad pan pizza styles like Sicilian, al taglio, “grandma pies,” Old Forge style, etc.) because how else are you going to cut a square/rectangular pizza?
Oh, and Quad Cities (as in the Quad Cities on the Illinois-Iowa border) tend to cut it into strips. So, one cut down the middle of the round pizza, and then a number of orthogonal cuts, so all the pieces have a bit of crust on them. I’ve seen this cut in NW Indiana, as well, though the name of the place escapes me.