With a game world split into discrete cells, especially large ones, there is another tricky design moment: picking hexes or squares. Squares are a bit easier to implement, yet naturally allow movement into only 4 directions. That is - squares create space with non-Euclidean topology and use Manhattan distance as a metric. Of course, trying to remedy that, you can also allow diagonal movement, opening a can of worms on its own, because units now move diagonally faster than they do horizontally. Surprise!
You can try solving that by further replacing the discrete number of action points with say a floating point number, subtracting 1.41421356237 for each diagonal move, instead of 1, but sqrt(2) is an irrational number, so there will always be some bias, unacceptable for a competitive turn-based strategy. Even worse, if you have two walls, sharing a corner, then a unit could still stick through it, even if it looks impassable.
Diagonal movement is clearly bolted on, but moving in just 4 directions would be too inaccurate and limiting for an strategy game, and that is why people prefer hexes to squares.
Yet with picking hexes, we have to make another important design decision: hex lattice can be rotated differently on screen. For example, Heroes of Might & Magic uses grid with vertically shared edges, while Battle for Wesnoth uses horizontally shared edge.
The case of vertical sharing allows for wide-screen friendly viewport, when each player has its own side of field, and units move without zig-zaging. Battle for Wesnoth maps on the other hand tend to placing two opponents at the north and south, because movement east and west will go in zig-zag.
Heroes of Might & Magic style grid also cheapens graphics production. In Wesnoth they have to draw units both facing south and north, while HOMM unit's sprite can be simply mirrored. That is in addition to nicer looking diagonal walls on castle siege maps. That saves both artist's time and and video memory.
Another decision is how to lay out hexes in a map. Obvious decision is to lay them in a square grid. Yet it would be a very bad idea to organize hexes as a square. A round world would be orders of magnitude better, as it allows easily making well balanced symmetric maps for any number of players, instead of just 4 corners or 4 edges of square grid. Round maps are important, because in hexagonal world area of effect and just larger structures too have hexagonal form. That is in addition to simplifying programming (it is a tricky task to pack hexes into a box).
That what they call good design - not fighting mathematics, but go along with it.
TLDR: my biggest mistake was picking squares over hexes. I would recommended hexagonal lattice even for real-time strategies. Unfortunately Blizzard doesn't feel enough competition to fix their competitive games and make the next Stracraft into a perfect game.
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Googling has shown that people fix this sampling bug using some advanced math, beyond my grasp. But I'm sure it can be fixed by using hexagon grid instead, and then sampling down to squares. Still for my purposes these subtle errors ain't that noticeable and diagonal walls look more gamey.
