Well, of course they do, but I guess that if you don't deal with cake pans all the time you don't think about it.
A 12" square pan is, well, 12" square. A 12" round will fit into that, so it's obviously a smaller amount of cake, and therefore a smaller number of servings. A 12"hexagon fits into the 12" round, so that's a little smaller as well (but not as much.)
So if you have a 6"-9"-12" square tiered cake configuration, it will serve more people than a 6"-9"-12" round tiered configuration will. That makes the three-tiered square more expensive than the three-tiered round, just by virtue of the fact that it's more cake.
Some bakers charge more per serving for square cakes than they do for round ones, and some don't. (I don't.) There's a difference between being charged more per serving and being charged the same per-serving cost for more cake. If your baker says that square cakes are more expensive, you need to clarify if they mean that they're more expensive because they serve more people, or because the price-per-serving is higher.
(And incidentally, there's no truth to the idea that you have to start with a round cake and cut the square shape out of them. They have these new-fangled things now called "square cake pans.")