You guys are looking at it all wrong, specifically, you're using the Euclidean metric (which only works in a Euclidean n-space) whereas Civ uses
Tchebychev distance as its metric. Under the latter metric, moving diagonally and orthogonally (with respect to the grid) are equivalent in distance, there is no geometric incongruity.
The apparent gain in distance while travelling diagonally is an illusion because you're seeing a Euclidean space but the units don't move according to the mtric of Euclidean spaces.
Thus, the only reasons to adopt a hexagonal grid system (which would operate under a Euclidean metric like would seem intuitive) are gameplay considerations. Since I don't have the patience to reply to every user who has voiced their (legitimate, in my eyes) concerns, I'll only reply to one post that particularly caught me eye, Lord Olleus's.
1) This can be mitigated rather easily by having the city expand into a larger square rather than a fat cross, perhaps leaving the corners outside of the city's production area.
2) This is a rather minor consideration and can be mitigated similarly to the solution for the previous point. In Tchebychev distance, squares are the equivalent of Euclidean circles and the equivalent of rings of hexagonal cells in that sort of grid.
3) This is a matter of taste. For me, granting that much power to blockades would be too much of a mechanic change. Fortifications have their uses, as strongholds away from cities where you can assail enemy forces from in the cases where such a position would be optimal. Anyway, it only takes two extra unit stacks to defend the flanks of a blockade and truly seal it.
4) You may be seeing a pattern here. Though the game is based in Tchebychev distance, many mechanics are designed with Euclidean considerations. They should have squares for ranges, but they don't. Anyway, this isn't a serious flaw in game mechanics.
5) Perhaps the most serious issue of them all, but in the end rectifying it is *not* worth a radical change in game mechanics.
Squares are the answer. =)