I always enjoyed the one city challenge in civ4, so I built a tiny map with 3 AI players and gave it a go. They seemed to do fairly well until end game. As you can see in the save they eventually stop building houses to increase population once they go over the 750 limit. It makes sense to think the AI is programmed to spead the food around smaller towns to level them up once their main city or cities reach level five, but if all their cities hit level five then they should continue to build houses. This is either a glaring oversight or it's bugged in some way. It's probably the latter considering they pretty much stopped improving their third and final city for some reason I couldn't figure out.
Also, in the city named Athens I noticed that I couldn't build improvements on some tiles (which didn't matter to me because I was planning on giving it to the AI anyways), and casting revive land didn't seem to do anything. Either this spell is bugged, I'm misunderstanding its effect, or there's some other bug preventing new buildings from being placed there. There was once a city there before the sov got taken out and it popped into nothingness.
I could pretty easily roll over the only AI left standing simply because they (apparently) hit the pop limit and could not build any more units, instead they're just pumping out a bunch of spiders. This is probably more of a concern for tiny, perhaps even small, maps, but I think it really gimps the AI towards the end of the game.
On an unrelated note, I've noticed that Gilden does a really good job of building parties, companies, etc. Pariden does a good job of pumping up their faction power, but I've seen them lose to other AIs with a far lower FP (maybe they aren't building many units due to their personality). Yithril has a tendancy to either neglect military techs or just flat out prefers to build lots of low level units.
I'd suggest you program the AI to be more careful with their champions like you did with their sov, but there's no point in doing that once they start gearing champions properly. Once that happens they should use them openly like they do now.