I believe that more information is always better.
I fully agree with this. In fact, this type of checks are great to make sure that there are no exploits.
I happen to disagree with the designs you call "obvious".
That is fair.
The 3 Arm + 1 Mot combination requires a lot of frontage for its firepower and is possibly oversized due to the aforementioned each division (not brigade) gets to fire once each round in combat. This means that two 1 Arm + 1 Mot divisions would probably outgun this combination despite being cheaper (but I haven't run the numbers yet to calculate equivalent battle-winning ability to know for sure).
As for frontage, I assume that you have it at one for armor no later than early 1940 at the most. This is a must for deploying it successfully, I think.
Your point about fired shots may be a valid one. I have assumed that 12 equal brigades will be able to fire about the same number of shots regardless of grouping, since you fire until you run out of shots before the cycle restarts. A small division may have a slight advantage in being able to fire off its shots first, but considering the length of the average combat, this should be a small effect (as pointed out by EntropyAvatar), more than offset by the, on the average, better leaders you can assign to a size 4 division.
If you compare formations with a 2:1 or 3:1 Arm to Mot ratios, the greater hardness (and hard attack) of the latter should significantly increase the combat effectiveness. Mot is not very different from Inf - except for speed.
The 3 Mec + Lt Arm combo will suffer the same problems, plus for exploitation purposes smaller divisions are more tactically useful. They allow you to split them off in different directions and potentially cover twice the ground.
It is true that a 2 L. Arm + 2 Mec division, which you can split into two 1 L. Arm + 1 Mec divisions, will provide you with combined arms bonus for both its temporary subcomponents. It is, however, also more expensive to produce and maintain, and in this case the idea is basically to use L. Arm to augment the already very attractive combat values of the Mec, while producing it in as small number as possible.
But compared with a size 3 division, which cannot be split into two divisions, a size 4 one will always provide you with greater tactical flexibility, even if you lose the combined arms bonus for half of the units when you fan out.