Wargames are among the most complicated board games in existence; proposing to make them more complicated would, therefore, seem insane: but my intent is to make them simpler by making them more complicated.
Almost all wargames (of the kind that use game boards divided into spaces, as opposed to the kind that use miniatures) use a board divided into hexagonal spaces.
This, besides being unfamiliar, makes it difficult to make moves correspond to the points of the compass.
I propose an alternative board design. I don't really think I'm the first to come up with this, though; I think the idea has been used in RPGs on occasion. What I advocate is using a board that looks like this:

The idea is that all moves begin and end on octagonal spaces, but in addition to orthogonal moves, diagonal moves are also possible. The movement cost of a move would be the total of:
1 x the Terrain Factor of the starting octagon 1 x the Terrain Factor of the ending octagon 2 x the Terrain Factor of any octagon passed through 1 x the Terrain Factor of any square passed through
The underlying logic behind this rule might be made clearer by looking at this diagram:

Now, all moves begin and end on white circles; moving from one circle to another, whether white or red, along a line counts as one step, and that step is multiplied by the Terrain Factor for the terrain type in which that line is located.
So moving from one octagon to an adjacent one, if all Terrain Factors involved are unity, requires 2 movement points, and a diagonal move requires 3 movement points. Thus, the design is based on using 1.5 as a crude approximation of the square root of 2.
Also note that the stream shown in the diagram is not navigable, and thus functions only as a barrier. A river that can be used for movement by boat would enter and leave the octagons in the same way as the road shown in the bottom of the diagram instead of the way the stream does.
Attempting to use designs like this:

to achieve true octagonal symmetry, perhaps following the Keplerian octagonal tilings described elsewhere, or even the Ammann-Beenker tiling, might lead to a gameboard whose connections follow this type of pattern, if the shapes other than the small squares and the octagons are not used:

Another thing in most wargames that could be simplified by being made more complicated, in my opinion, is the Combat Results Table.
This table shows what happens for different die rolls based on the ratio of the forces of the attacker and the defender; it may look like this:
1:3 1:2 1:1 2:1 3:1
1 AE AE AE EX EX
2 AE AE AE EX EX
3 AE AE EX EX EX
4 AE EX EX EX EX
5 EX EX EX EX DE
6 EX EX DE DE DE
It has two problems. One is that one has to remember to round off this ratio in favor of the defender. Another is that sometimes improbable results appear in the table in order that the battles not be without risk for either side.
So how I would improve the typical CRT is by making it larger.
Instead of rolling one die to resolve combat, I would use the total of three dice, allowing a distribution of results approximating the normal distribution, and allowing improbable results to be possible but unlikely.
Instead of having columns, each one headed with a particular ratio, I would have additional columns between each pair of exact ratios; if the ratio is between 1:3 and 1:2, one looks in the column between the 1:3 column and the 1:2 column.
Thus, one would obtain tables that look like this:
1:4 1:3 1:2 1:1 2:1 3:1 4:1 5:1 6:1
3 AE AE AE AE AE AE AE AE AE AE AE AE AE AE AR AR AR AR AT
4 AE AE AE AE AE AE AE AE AE AE AE AR AR AR AR AR AT AT XD
5 AE AE AE AE AE AE AE AE AE AR AR AR AR AT AT AT XD XD EX
6 AE AE AE AE AE AE AE AE AR AR AT AT AT XD XD XD EX EX EX
7 AE AE AE AE AE AE AE AR AT AT XD XD XD EX EX EX EX EX XH
8 AE AE AE AE AE AE AR AEDH EX EX EX EX EX EX EX S S XH DR
9 AE AE AE AE AE AE AR AEDH EX EX EX EX EX EX S HX XH DR DR
10 AE AE AE AE AE AR XH HX EX EX EX EX EX S HX XH DR DR DR
11 AE AE AE AE AE AR HX S EX EX EX EX S HX XH DR DR DR DR
12 AE AE AE AE AR XH S EX EX EX S S HX XH DR DR DR DR DE
13 AE AE AE AE AR HX S EX S S S HX XH DR DR DR DR DE DE
14 AE AE AE AR XH S EX EX S S HX XH DR DR DR DR DE DE DE
15 AE AE AE AR HX EX EX S S HX XH DR DR DR DR DE DE DE DE
16 AE AE AR XH S EX EX HX HX XH DR DR DR DR DE DE DE DE DE
17 AE AE AR HX EX EX AT DEAH XH DR DR DR DE DE DE DE DE DE DE
18 AE AR EX EX EX AT AT DR DR DR DE DE DE DE DE DE DE DE DE
AE: Attacker Eliminated
AR: Attacker Retreats
DR: Defender Retreats
DE: Defender Eliminated
XH: Exchange Half (weaker side eliminated; inflicts casualties half its own size on stronger side)
EX: Exchange
XD: Exchange Double (weaker side eliminated; inflicts casualties twice its own size on stronger side)
AT: Attrit (weaker side unscathed; inflicts casualties its own size on stronger side)
HX: Half Exchange (both sides suffer casualties equal to half the size of the weaker side)
S: Spent (combat ends for both units for the turn without casualties)
AEDH: Attacker Eliminated, Defender Halved
DEAH: Defender Eliminated, Attacker Halved