I kinda see what your saying, but a little micromanagment makes the game fun. Of course the game would be balanced. I don't see how adding more units would change that. I didn't say special units or anything (but that is an option).
All units in Civ IV are more or less special. Even in vanilla. You have axemen as your counter-melee units, swordsman as a city raiding force and later on, riflemen to take and hold cities weakened by cannons, cavalry to take enemy workers and pillage their iron mines and a grenadier or two to pick off enemy riflemen.
Let's concentrate on the pre-gunpowder eras. You have basically the following units:
Axemen and crossbowmen for countering melee
Spearmen, pikemen for countering mounted units
Mounted units for stealing workers, pillaging and mobile attacks
Archers and longbowmen for holding cities
Swordsmen (and macemen) to take cities
Catapults and trebuchets for smashing enemy stacks and cities
Basically, your warfare goes like this - you raise a stack of your grunt unit: swordsmen (or macemen if you have them already), then you give most of them city raider promotions to maximise their strength against enemy cities, give them some siege weapons and put a couple of spears/pikes, anti-melee units unless you use macemen, and archers to protect the captured cities. And then you just roll over your enemy.
Should we add a new unit, it would be either a grunt unit that is the main force of the invasion (high strength units), or a specialist unit that excels against a certain unit type(lower strength but bonuses good for stack defense). New grunt units aren't needed, as people already whine about some of them being too short lived. Also, they're the least interesting of all units. But we can't eliminate the grunt units, simply because that would make the game play like rock-paper-scissors and nobody wants that. New specialist stack defender units would add nothing (as everything already has a counter) but the
unfun element of building a couple of additional units in your offensive stack.