Look at the formulae again.  9 attack = 9 damage. 3 attack = 3 damage. (minus defence of course). This thing is very OK.

That may change things a bit, but that's not quite what I've seen ingame at times.  I hope you are indeed right about that (attackers attack value instead of defenders), because that would be a little better... Of course, if you have a 6-man unit with said weapons, well you essentially multiply all damage by 6, before any bash modifiers, etc.. 

End result is still the same.  Attack values are vastly outstripping defense values and hit points, hence the significant number of one hit kills I am still seeing.  This is why the term 'glass hammers' has been applied so often in many critiques of this game.

As for the 'divide by 0', a min divisor of 1 is easy to code in.  As I don't have access to the code, I can neither confirm or deny, just comment on what I've seen ingame.  And it seems to me that there is still a good amount of cheese in the game, but that may just be me.  Hence my inquiry here.

Early units are still very quickly massively outclassed in this game, however, so that point still stands regardless.  There isn't really a 'increased hit point' mechanism that parallels weapon development.  Even a bump from level 1 to 2 isn't going to make much difference as it currently stands, so fresh/untrained units are very much glass hammers in the later game.  Experience helps some, but all this does is essentially reward the uber stacks that are earning experience, while replacement defending forces essentially have no such experience to fall back on, once the more experienced defenders (if any) are taken out.  Hence the steamroller effect we hear talked about so often.

In a number of other 4x games, I see 'lightly armed/underclassed' units making a much better account of themselves against heavier/stronger foes than they do in Elemental.  Personal preference, I guess...

It should be rather easy to test. All you need to do is build something with low attack and 0 defense and throw it away against a random monster with high attack. If you see something that doesn't fit in the rand(0.5, 1)*A^2/(A+D) range when using A = attacker's attack, D = defender's defense, check the attacker to see if it has Overpower (multiply damage by number of figures in target unit), Bloodthirsty (+25% damage to damaged targets), Enmity (+25% damage to opposite-alignment targets), or any similar traits, or see if it has a weapon which gives +X% damage per successive successful attack. Also make sure to include armor penetration, and make certain it wasn't a critical hit, and preferably use a single-figure monster for this test, because individual figures can miss even if the unit as a whole makes a hit, which could screw with keeping things in your damage ranges. Also also make certain that this monster's attack was a physical attack rather than an elemental attack (fire, cold, lightning, poison), because elemental attacks are unaffected by defense, and if it has mixed damage types, you'll have to try to separate it out - elemental damage does rand(0.5,1)*A damage, but it gets reduced by the target's resistance to the appropriate element (or increased, if the resistance is negative), so you can at least get an idea of how much of the damage comes from where, but it's more of a pain than with the pure physical attack case.

An alternative test to the above would be to mod one of the starting sovereign weapons to have a very high attack, and use that and see if you ever get ludicrously high damage numbers out of it (on the order of A^2 rather than A) when attacking low-attack 0-defense enemies.

I will say that I've never seen anything that even remotely looked to me like the damage function goes to A^2 rather than to A as defense goes to 0.

I wasn't disagreeing with the point of your post. I was explaining that, to the best of my knowledge, your description of the damage mechanics is inaccurate, and providing a correction.

I feel that this is more a problem of including health as one of the level bonuses, rather than leaving everyone at a fixed health that you can balance the weapons around and improving the survivability of higher-level units by, say, granting +1 dodge per level. At least that way, the high-level units can't just shrug off successful attacks made by low-level units. I think you'd probably also want to change the health recovery mechanic; healing at 1 health per level per turn makes it even harder for low-level units to successfully pile enough damage on a high-level unit to seriously threaten its existence, and makes the Infirmary improvement much less interesting.

I think this is an issue with the set of technologies that Elemental provides. Regular units only really have 3 choices in armor sets, and those choices offer enormously different protective qualities, with variably painful initiative penalties that can be largely ignored with appropriate trait or weapon choices, and negated by a city enchantment. I would certainly have liked for elemental to provide a real set of light/medium/heavy armor options at different stages in the tech tree rather than what we've got, but I don't know that that boat was ever on Elemental's horizon.