Mounts with troops in heavy armor should either require breeding grounds(improvement that requires a stable and lvl 3 city), or get a move penalty.
The breeding grounds improvement should unlock better mounts. There could also be a racing horse which is quicker.
Empire should lose wargs, which should become a food source instead, and gain the ability to use horses themselves. Horses are rare enough that it doesn't need to be split up.
The warg resource: maybe empires could gain a similar improvement that would unlock warg mounts instead of just being a food source. You could have similar things for other sorts of mounts (which would be modded in, I'm shocked we don't have a bear mount mod yet)
In general, I'd like to see more buildings in Elemental down the line require lvl x city + resource. The specialist stuff should be strong enough, and the bonuses for leveling cities enough, to discourage ICS, but you'll need something to equally discourage OCC (one-city challenge).
I think another way this can work is making some of the logistics/training techs require buildings like barracks or training posts and the high end versions to require higher level cities in addition to boot. (maybe equal to level of city)
I agree on the specific modifiers. If you're going to have a fairly mundane model (which I'm fine with, only so many pointy-eared pretty-boys I can stand), you need some wargamey-type stuff in there. I think the fanbase here would respond positively to that.
Another thing down the road I'd want is AOW-style levelling up, where you can gain an ability on level up. Doesn't have to be something dramatic, a modifier could work as well. For example, a ranger-class hero (heros, especially adventurers should have classes)- could gain charm animal to get a chance to convert animals defeated in battle, or marksmanship bonuses to increase archery to-hit and damage, or poultice skills to improve healing rates. Warriors might get a weapon mastery skill to improve stats with weapons, or something making them immune to counterattack, a toughness skill that lets them roll their defense multiple times to get the best result, etc. These probably should be in addition to start bonuses.
One idea is instead of just a flat move penalty, have armor give encumberance, which reduces dex and move speed for different races differently.
That may be too complicated for base Elemental (I could see a mod trying to do something along those lines though)