Hey
Xenon14, I think I can give you at least part of the answer that you're looking for. A lot of wafer processing steps in the fab involve spinning the wafer (such as depositing photoresist onto wafers before they are run through photolithography). As you might imagine, spinning square or rectangular wafers isn't a very ideal situation.
However, I think in order to best answer this question, you would have to look at how the wafers themselves were manufactured. I'm not very well versed on this topic, but perhaps a senior EE student or fab technician could answer your question completely. The way I understand it, silicon wafers are manufactured by sort of "pulling" a large silicon rod out of a circular mold, grinding it smooth, then cutting each wafer up individually, followed by polishing it smooth. Again, this process is much easier to perform with circular objects, as opposed to something square or rectangular.
Here, I even looked up a site that tells a little about how silicon wafers are manufactured:
Silicon Wafer Production Steps
I hope I answered at least part of your question, and I hope that someone with a little more knowledge than I can come in fully explain everything.