Another thing that could be implemented would be an 'ambush' feature to each unit, like fortify. When a unit is lying in ambush mode, they'd be invisible to enemy units potentially with a chance of discovery [not cumulative with multiple enemies present on the same tile]. Ambush would count for a few first strike chances [say 1 per turn in ambush mode to a maximum of 5, subject to play-testing and balance of course], even for units that would normally not receive any. And the number of turns in ambush mode could decrease the likelihood of being discovered. Cavalry would not be immune to the first strike of ambush.
Ambush mode would get the defensive bonuses of terrain as well, and if the SoD 'discovers' the ambush at the onset of attack, then the units lying in ambush would not gain the defensive bonuses of fortify, or the first strikes of the ambush. Furthermore, larger numbers of ambushing units in the same tile increases their chance of being discovered negating the effect of an ambush.
After a successful Ambush, the surviving Ambush units would be scattered on the adjacent tiles around where the battle occurred, subject now to movement 2 cavalry counterattack, or at the beginning of their next turn to flee and regroup using normal movement. Another thing to consider would be ambushing units attack the units in a stack they match up best against instead of worst because technically it's the attacker who's moved into them, making the ambushing units the defenders. This could prove to be absolutely devastating to a SoD if you lose 3-4 city raider units each time during a successful ambush. But the ambushing effect would be counterbalanced by the effect of multiple ambushers on a single tile decreases their chance of a successful ambush.
This to me would make several things relevant again. Scouts and freelance mounted units on the offensive would increase your chance of finding units in ambush, so it might be worthwhile to build employ them. It would make some of the most critical battle fought outside of the capture of cities. It might make feints useful and battlefield tactics useful. [hit and run cavalry to funnel a SoD into ambush for instance]. It may allow the game designers to finally tone down the ******** defensive bonuses archers get for city defense which makes a stack of doom necessary offensively in the first place!
I've been a big proponent of taking civ combat outside of the cities, and this is just an extension of that. How many ancient wars were decided on battlefields, and not on the city walls? That's the kind of warfare we should be aiming to recreate.