I agree, civ is a strategic game, the addition of flanking tactical side of battle does add micromanigment, and furthur handicaps the already handicapped AI, thus taking away from the game.
IMO there is already a fair bit of strategy in combat
-chosing which units/promotions to use in a situation
-proper use of collateral damage
-if the opponent doesnt have many catapults: hitting the opponent with catapults first, then letting them take a move, so that your units will be defending with the strongest unit (eg a spear kills a damaged elephant etc)
-purposely sacrificing a single unit out in the open as bait for the opponent to kill, thus seperating some units from the opponents stack to kill on your next turn
-suicide chariots to cut enimy supply lines, making it possible to take down a city
-luring the opponent into your land where you can use hit and run with siege weapons(and air if in modern age), also limiting WW due to casualties on your teritory, purposely softening up the opponents arsenal before stepping onto their teritory.
-purposely chosing which units to attack with so your sacrifices die while the highly promoted ones gain even more promotions.
in many situations its best to use some strategy instead of simply a SOD, this becomes even more significant in the higher levels where the opponent gets a tec lead, meaning you are fighting cats+achers+sword+phants+spears vs knights+mascemen+longbows etc in overwhealming numbers. the only way to succeed is to play a few gambits to try to even the score.
all this is in the spirit of civ, having significant strategy in battle, as stated promotions cover the unit abilities. as stated before, if i wanted battle tactics i'd go to one of the numerous RTS games. adding it here just adds another headache to the game. i'd hate to check the unit direction of every unit every turn on a huge map modern war, ouch!