What reasons would a designer want to employ squares over hexes in a battle simulation game?
Well one point towards squares is simplicity. It is a much easier system to grok (outside of weird rules for diagonals)

The most important thing to consider is what your playing field is. If you are talking about a mostly open plain with very few obstacles, then a hex field is great as it avoids the diagonal rule cleanly.

However if you were going with, say, an urban layout, then a hex system would have a harder time with all the straight edges (not impossible, but difficult) while also not helping too much, since diagonals aren't a huge deal with hallways.