I'd definitely hesitate to declare war with only Archers at my disposal for another reason: the AI loves to pillage. On flat terrain, even a Chariot (the AI also loves mounted units) is a decent match for an Archer, even a fortified one, and can you really build enough Archers to camp atop every single tile improvement? You could find your tile improvements gone and your economy in ruins in such a situation.
I actually went and tried out a few archer rushes just for the heck of it. The problem is not that the AI pillages. Pillaging just isn't an issue, period. A couple of scouting warriors might try, but anybody else is going to run smack into the steam of reinforcing archers heading to help your attacking forces and their horses are going to be pillaged or owned by you long before they get a useful number of chariots.
The real problem is that it takes about 3 attacking archers for every defending archer to take an early game city. Getting there with 4 when they've got 2 isn't enough, you need 6. In my games, I generally ended up not having enough to take their capital and having to wander around their territory, pillaging and taking their other cities with my archers. I'd bring in more archers to take their capital and they'd build more. I'd lure a few out and kill them and they'd build even more. I tended to finally crush them, once and for all, shortly after I got the bronze or iron connected and running. CR axe vs archer? No contest.
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Anyway, some general comments.
With regards to pillaging: Although in some cases, the suggested pillaging stack works well, in many cases my preferred pillaging strategy consists of 2-4 groups of 2 (or 3, once in a while) mounted units, with promotions specific to melee or gunpowder (whichever looks most dangerous). The enemy can possibly attack and kill a few, but I operate them close together, so whoever did it then gets killed by the other groups. If some units get damaged, they can quickly be escorted to safety, or even leave on their own. SInce I don't have a lot of different types, casualties mean I can consolidate groups without problem. Prioritizing targets is not much of an issue, I simply remove everything, including the roads. Of course, the drawback is this only works if the enemy doesn't have technology that would be effective against your horses in sufficient numbers (the AI rarely builds enough pikes, for example).
With regards to using a giant stack o' doom, yes, sometimes it will work, but sometimes piling everything together will lose you an army. I often break down into smaller stacks and the best I can say is that it works. It's not always the best choice, but that depends on how the tactical situation looks. Here's an example:
Suppose I show up at a city with an attacking stack of 15 units. The enemy launches an unexpectedly heavy counterattack with 4 siege engines and 4 other attackers. 4 siege engines means that most of my troops are going to take substantial collateral damage. They might even kill a guy or two. Then the other attackers hit me. Most of my best units are pretty beat up, so Most of those attackers will win. I lose 3-5 units and will need 3+ turns to fix my forces up. Many of the enemy attacks were successful, so they have some guys who can try again soon, plus they have time to bring in more siege and more attackers, keeping me from getting fixed up. At best, I probably won't be able to take the city without reinforcements. At worst, they keep on hammering and I lose the stack. It's happened more than once.
Now, suppose I'd broken my forces up into groups of 3. The enemy can probably kill one totally, and leave the next one with a single damaged catapult. But most of their collateral damage will be wasted and I have 3 undamaged stacks. I can quite possibly take the city out from under them the very next turn, allowing followup units to sweep along their roads and mop up.
Actually in most circumstances 3 is kind of light, I'd usually use 4 or 5, but it depends on the situation. Another advantage with smaller groups is that the advance can continue as soon as I've got a few guys who are healed up. I don't need to wait for the whole stack. I can possibly move out the same turn I take the city, rather than waiting for the whole group to be combat ready. I also find it helpful, if non-hostile roads permit, to send a catapult ahead, so that when I arrive, the defense is already toast.
Now, I may take a few more casualties this way (some of the time), but I also get cities taken quicker, which gets them producing for me quicker and the war over with quicker.
If the stack of Doom always works for you, I think it is because you are fighting AIs who are so totally outclassed that pretty much anything you do is going to result in a win. If all they've got is a catapult and 3 archers, there's nothing they
can do, except perhaps pull the whole lot back to the next city and gift this one to some other civ to piss you off (neither of which the AI ever does).