The thing you have to realize about stacks in civ 4 is that they're NOT countered by collateral damage. Maybe that was the intention, but the way it's implemented, splitting up a stack won't reduce your collateral damage at all. Well, not unless you split it into less than 5 units, which is too small of an army to do anything.
The REAL counter to stacks in civ 4 is the fork- the ability to threaten multiple cities at the same time. If you've got an invasion force that can potentially hit 3 different cities or resource tiles, and they can't counterattack in time, they'll have no choice but to split up their army into three pieces. The more places you threaten, the more they'll have to split up their army. The "stack of death" where you put all your army in one tile just doesn't work.
Unfortunately, the AI in civ 4 still leaves a lot to be desired. It doesn't try to threaten more than 1 city at a time, and it always leaves behind a garrison in every single city. So, when fighting the AI, you don't need to worry about being forked, and there's little point in sneaking in to take out vulnerable cities. The giant stack of death works pretty well against the AI- but only because the AI is so stupid and has such monstrous production advantages.