Gentlemen, may I turn your attention to two facts that haven't been addressed so far?
First, why is it that despite what both Polybius and Livius state, virtually all modern representations feature a east-west facing armies? True, the river for the most part crosses the Cannae plain in an eastern direction, but that may not have always been the case. Furthermore, a river doesn't have to be very wide to represent an obstacle. In fact, the banks would be much more important than the river depth itself.
Second, and that's actually in a way a modification of the KISS principle in my opinion: By doubling the depth and at the same time eliminating the spaces between each maniple, Varro constricts the eight legions under his command(actually sixteen - eight Roman and eight Allied foot) to the same frontage that a consular army(2+2 legions) would have if deployed in the usual order. If Varro was indeed a commander of limited experience as he has been portrayed, having the normal frontage would simplify immensely battlefield communication as far as he was concerned. True, the formation would've become very unwieldly, but that was alright with him, since he must have expected the cavalry to pin and hold the Carthaginian horse, while the legions punch through the enemy center as they had managed to do in the two previous battles against Hannibal(At Trebia the Roman center managed to break through the Carthaginian line, despite being attacked from the back and the sides; At Trasimene the Extraordinarii and/or the Roman vanguard slaughtered their way though the ambush, which might have been what Hannibal wanted, since the bottlestopper were light troops iirc.). The fact that just the first couple of ranks would be able to throw their pila would be compensated by the quadruple depth of the velites present. So from the PoV of Varro, it would be like a normal consular battle, except that the cavalry wouldn't break and the infantry would have much more momentum and would require much less time to break through the enemy line.