Hm... not a bad idea. There are drastically different effects for each type, however, and relatively few Elemental Damage types that would ever be defined. I wouldn't think we'd have more than 6 such types ever and each one would have a very different effect on units which would mean each one would have unique associated tags as it is.
For example, Cold Damage (if the unit is not immune to the effect) reduces Dodge and Precision by the same amount as the damage until its healed, the added effect resisted by Endurance (this part would be rather generic).
But Heat Damage would instead Fatigue and Tires at a ratio of 5/1.
Then Electricity Damage would probably have a stunning effect for a number of combat rounds (really would only be applied in combat) at a ratio of 15/1 or something like that (will need to balance it out properly) and/or would completely ignore armor.
Radiation Damage would probably just add to a Radiation Property (something I've been considering for a while) that would naturally bring its own Auto Assigned negative promos at higher levels to represent that poisoning. (so would not be developed any time too soon either...)
How would this kind of vast diversity of effect benefit from such a generic approach?
It allows them to be modded, so if you wanted a new damage type (poison say) you could define what combat properties of a unit it interacted with.
However, this strikes me as very similar to afflictions - why not have a damage type simply inflict an affliction promotion of the recipient, which is already generic and can do whatever you want based on what promotions can do. So you define a new DamageTypes and the XML for those defines the afflictions that different amounts of that damage type inflict.