I agree with the OP. Right now the game is all about getting powerful first strikes in. It's not all about the damage though. It's tons of little things that have made it so. Like starting closer, and starting with troops. The new initiative system has also allowed players to super buff damage easily using traits, and we have all this nice new abilities that allows us to cross the map in 1 turn like rush and berserk, or hit multiple people like cleave. This also increase the speed of tactical combat.
Here's what I think needs to happen.
General:
-Cut weapon damage by a bit, not too much. Mostly just bring down the outliers.
-Make sure units start in defend mode.
This would be amazing, would really give "+defense while defending" the boost that it needs
-Boost base champion hp. Not troops.
?
-Get rid of fortress improvements that give charge and impulsive.
I agree, having fortress give those traits promotes making armies that are entirely axe/spear cavalry or ranged units respectively.
Maybe "Defensive Drills": This unit gets +2 armor for every soldier in the stack. (so up to +12 armor, changes in battle as soldiers are lost and healed in the stack)
Maybe "Phalanx": For every allied troop adjacent to this unit, enemy troops swarm with 1 less unit. (So if an enemy tries to swarm with two of his adjacent units, and you have an adjacent unit, only one of his units can swarm onto his attack.)
Maybe a gladiator arena city that gives "Ex-Gladiator": +1 attack +10 dodge to units trained in this city. (And while I'm on the subject, it would be cool if lucky gave a flat +15 accuracy +8 dodge to all troops, instead of that snowballing percentage)
Maybe an assassin city that gives "Assassin": +15 crit chance, +10 dodge, +2 initiative, +1 movement, but the city can never train mounted units or units with armor heavier than leather. (Actually, I'd really like to see fortress types like this, to really give a reason to have more than one fortress making your armies)
Maybe a +1 essence fortress.
Just some ideas.
-Nerf cleave and impale so their secondary targets take less damage, unless you have the right traits.
Maybe cleave should do 50% damage to secondary targets (and 100% to the primary), or 70% to all 3 targets. Impale should do 85% to both targets I think, because I often use impale to reach units that are normally out of the spear's reach, and I think it's a cool mechanic that they can do that.
Also, I think that the sword counterattack should be 100% damage, or at least 80% damage, because it occurs after the unit is hit anyway, so it ends up doing far less damage than the attack that triggered it (if the person even triggered it, instead of using cleave/impale/bash/spear/ranged/whatever to keep counterattack from triggering.
I think that warrior should get a trait that lets them counterattack before the triggering attack. Mostly because I really feel that both sword and warrior are underpowered at the moment.
Balance out traits:
-Remove strength for troops.
-Make muscle give -1 initiative.
Obviously something needs to happen here, since currently they do the same thing for different costs. 
-Reduce charge to +1 movement and +2 damage.
I would say +3 movement +1 or +2 damage (any cleave or impale nerf is going to help nerf charge armies anyway), because this entire trait is useless if the unit that gets it cannot reach the enemy on the first turn. This tactic needs to be brought down to the level of other tactics, and I think reducing the movement to +1 will just stomp it into the dust (and further promote making every single unit you make a mounted unit).
In fact, if units are made to all be defending at the start of a battle, and cleave and impale receive nerfs, I think charge won't need to be nerfed at all.