I think Hex would add more complexity and mobility. Might have to adjust LOS rules a little.

Apart from being a little easier to count diagonal ranges, can't see any advantage and would need a whole new set of rules, board and terrain to play on.

Hexes would actually reduce mobility, and create the need for alternate building as well as line of sight rules.

The square grid allows movement in eight axis, as opposed to six for hex based movement. While additional diagonals cost more movement, that is to correct the actual distance covered being 1.4 times the distance of orthagonal movment, so it makes sense. Rounding catches you fairly quickly, but most units don't have enough range, or have unlimited range, for it to cause problems.

Buildings would need additional rules, as a normal building can fit in squares, but few buildings would fit properly in hexes. The extra space would have to be accounted for. The size of openings would have to be accounted for to allow specific units to enter, exit, or draw line of sight.

The only advantage for hexes would be if someone already had a game mat with hexes that were about the right size.

For that, fake some simple building rules, count each hex as one space, and still take line of sight as center to center. Crossing the corner of a blocking hex would still give cover.

The simplest option for buildings would be to ignore the extra space outside buildings, and assign what openings can be used by walkers before play begins, and make sure people know. Otherwise, line of sight would stop one hex in as with spaces, and would have to cross through an opening to alow fire into or out of the building. Entrance to or exit from a building would have to come from a hex facing the opening.

I see your points. I agree that squares are simpler.