It doesn't make it fair; it merely makes it different. Maybe a better approximation to Euclidean geometry, but once again, the point of having a map isn't to be a geometry simulator.
When talking about correlation between game movement points utilized and actual distance travelled, then the word
fair is IMHO appropriate.
It's silly to lament that some lone mountain doesn't get in the way of travel. If it's not in the way, it's simply not an obstacle; don't worry about it.
You still fail to understand that our problem with square tiles is the inconsistency in this.
The X represents an obstacle, o is your position and T is the destination. In both the following situations you want (for whatever reason, this really is irrelevant now) to move from the starting position to the target destination. In both cases it is two tiles away with the obstacle being exactly in the middle. The situation is exactly the same. But in the first case you have to spend 3 moves, in the second case only 2 moves. In order to get 2 tiles away behind the very same obstacle. The only difference is that you approached in from a different direction - and this only difference is in fact caused by the properties of squares, because squares have this inconsistency.
+---+---+---+ +---+---+---+
| T | . | . | | . | . | . |
+---+---+---+ +---+---+---+
| . | X | . | | T | X | o |
+---+---+---+ +---+---+---+
| . | . | o | | . | . | . |
+---+---+---+ +---+---+---+
And let me draw you something more, something I already talked about. Let's say you have a boat with 1-tile visibility range and want to quickly go west to find another continent. In sounds natural to move in a straight line (getting somewhere fastest = move in a straight line, that's common sense for everybody). And you expect do uncover a 3-tiles wide line because of the 1-tile visibility. On the next picture * represents positions of the boat and circles represent uncovered tiles. In both cases you spent the same moves, but in the second case you travelled much longer distance and uncovered considerably more tiles, for no additional cost (well, micromanagement is a good point, but strictly speaking the cost is not quantifiable).
+---+---+---+---+---+---+---+---+---+ . . . +---+---+---+---+---+---+---+---+---+
| . | . | . | . | . | . | . | . | . | . . . | O | O | O | . | O | O | O | . | . |
+---+---+---+---+---+---+---+---+---+ . . . +---+---+---+---+---+---+---+---+---+
| O | O | O | O | O | O | O | O | O | . . . | O | * | O | O | O | * | O | O | O |
+---+---+---+---+---+---+---+---+---+ . . . +---+---+---+---+---+---+---+---+---+
| * | * | * | * | * | * | * | * | * | . . . | * | O | * | O | * | O | * | O | * |
+---+---+---+---+---+---+---+---+---+ . . . +---+---+---+---+---+---+---+---+---+
| O | O | O | O | O | O | O | O | O | . . . | O | O | O | * | O | O | O | * | O |
+---+---+---+---+---+---+---+---+---+ . . . +---+---+---+---+---+---+---+---+---+
| . | . | . | . | . | . | . | . | . | . . . | . | . | O | O | O | . | O | O | O |
+---+---+---+---+---+---+---+---+---+ . . . +---+---+---+---+---+---+---+---+---+
Making a big deal that it interrupts travel along one of the six special directions of a hex grid is silly, because it's rare that some unit will want to make that exact journey. It's even sillier in 1UPT, because even if individual units can go around the mountain, it still puts a kink in the motion of a group of units.
You still repeat that a problem is not a problem if it doesn't appear all the time. I cannot agree with it. Hexes are consistent and such problems don't appear at all. On squares this problem exists.
If your car sometimes starts and sometimes not, it's not a problem?
Human eyes are naturally good at scanning horizontally and vertically.
In fact not. Orthogonal structures and objects are related ONLY to human-made objects and only quite recently (compared to how long have people existed on this planet). Around us in nature, where can you find anything square? There are much more natural shapes like spheres. And how do bees make their constructions? Why are they using hexes which are in your eyes much more complicated, and not squares with all their advantages?
Keyboard input fits naturally with square grids.
I agree on this particular point. I don't even know whether you can move the units in Civ5/6 using keyboard, but it would be very unintuitive anyway. And I used keys in Civ1 (didn't even have mouse back then) and Civ4 (sometimes).
But Civ4 uses perspective camera and you can even rotate the view (if I remember correctly - please forgive me if I'm wrong). How's the keyboard movement so much natural then, when up isn't exactly up?
And what about a very typical axonometric view, for example in Civ3? Shall the diagonal keys (1, 3, 7, 9) on numpad represent diagonal movement on the grid (which would sound logical) or the orthogonal movement which physically better represents the directions? I remember I always had problems in such games and used mouse all the time instead.
We're educated in a variety of contexts to understand things relative to an orthogonal pair of coordinates.
Because it's great for mathematics and geometry. That however doesn't mean that it is the best choice for everything.
I however agree that hexes feel strange at the beginning, because we aren't used to them so much. But there are many advantages to them and you get used to them very quickly. And the world looks more natural, because land and nation borders modelled on squares look too artificial. Look on a real map - coast will be straight with orthogonal angles only on very short distances (luck). And even national borders are orthogonal and straight mostly only in the USA and at some places in Africa - because these borders were artifically drawn by people in an office on a blank map after some deal. Typical borders copy rivers, mountains, villages, represent thousands of years of battles etc.
It's easier to determine exact distance in a square grid.
No, it's the exact opposite
Distance in a square grid has a very abstract meaning. You can count tiles between two tiles. But distance is different horizontally and diagonally.
As an aside, I think a large part of the feeling of the significance of the gameplay difference between hexes and squares (with 8-way movement) is because the 'special' directions on the square grid are the four diagonals -- but those aren't the directions people compare to the hex grid's six 'special' directions.
If hexes have 6 directions in total, how can these 6 directions be special? That's the problem, all 6 directions on hexes are the same. If all people are blonde then nobody with blonde hair is special (because of his hair).
However, 4 directions on squares are "natural" and 4 directions are "special" or "different", because they have very different mechanics.