Not sure how people take out cities with walls + garrison with just archers, at least not unlike you have absolute open terrain surrounding it. I find the AI is pretty good at getting up ancient walls, and they also get chariots or whatever quite early, which means their garrison strength goes up to 30 or something like that. If they manage to place an archer or maybe even two in or next to the city, they will pretty much kill my archer in one turn, or at least take it so far down in health that I need to move it back to save it from dying after one shot. So unless I have something like 20 archers and perfectly navigatable terrain, there's no way I can bring down ancient walls just with archers.
I admit it runs kinda goofy.
Some games, like you say, they have walls up in their whole empire.
I run into games where they are getting barbed or another AI is at war with them.
Sometimes they just don't build walls.
I certainly do not take an empire with archers when they have walls up.
So once again it all depends on what Civ you are playing and playing against.
Map and Settings make the game play different as well.
I just played a game two days ago where Russia was getting Barbed like no other.
I stole two settlers from them and took their empire with archers, warriors and chariots.
It didn't hurt that the Barbs were using catapults on Russian Walled cities.
Ended up with 5 of their cities and 2 of their settlers.
I just finished a game where Dido and Matthias were at total war for the first 100 turns.
I ended up taking both empires with muskets, cannons and a couple bombards.
Of course it helps when they are Dark and you are Golden.
Each game differs but I run into the some similar scenarios as already discussed in this thread.
My comments were not meant to be absolutes.