There are trade-offs involved with any paradigm, be it squares, hexes, even with continuous movement. The question is rather: what fits your design intent best? The player's experience is what counts in the end.

Squares and hexes are discretized environments. Again, this brings benefits and drawbacks. The advantage of hexes in this scenario lies in the fact that they often provide a richer medium for quantized movement in games. There is nothing inherently complicated about simulating movement and areas of effect in hex maps, neither for computers nor for humans.

If your game requires straight lines to be modeled perfectly, both hexes and squares provide two "clean" axes for that. Realism is a relative goal in a war game. It's all a set of models in the end.

Moving in straight lines using arbitrary angles is also not something that can realistically happen on battlefields.