OP, you ask the wrong question. The expansions very much improve the depth and replay value of the game. Really, it is remarkable that the lame AI does not make things worse, but it is the same AI you faced in cIV, so its not like things have gotten worse.
As mentioned, it's not that the AI has gotten worse, it's that the expansions' additional content opens up new ways that it can fail.
It's also important to remember that this is not the same AI as in cIV, since Civ5's one-unit-per-tile makes AI unit handling a nightmare. If you don't believe me, have a look at the source code yourself: things becoming incredibly complicated when an AI unit is blocked by another AI unit that can move, but if it moves out of the way, it will have less moves left, possibly not being able to attack the common attack target, etc. etc.
[...] (not up the level of a skilled human, certainly, but it no longer suicides its units into cities with lemming-like single mindedness).
My AI vs. AI test games say otherwise: given the right circumstances, the unmodified AI will gleefully sacrifice its melee units into a city, only to withdraw when it realizes that it doesn't have any more melee units left with which to take the city.
The strategy and depth of the game are greatly improved by religion, ideologies, and the World Congress.
Strategies are improved, yes, but their depth is not. If depth is supposed represent how many viable strategies there are and the nuances between each one (as well as what strategies to start with and when, if ever, to switch to a different strategy mid-game), BNW and G&K have just as few viable strategies as vanilla Civ5 and transitioning between them is often just as unnecessary as it is in vanilla Civ5; this is especially true at higher difficulty levels.
Note that things change quite a bit with multiplayer, most importantly because everyone in the lobby has the same idea of what strategies are viable, so the nuances between individual versions of the same strategy become more pronounced. Since there is more room for creating different versions of the same strategy with the expansions, the game indeed becomes more deep.
Religion in Civ5 is just another way to get empire-wide bonuses, like policies, albeit through a different currency (faith instead of culture); the main distinguishing feature is that faith costs increase with game time rather than with empire size. The only depth it adds is "should I attempt to compete in this path for empire bonuses or not?", to which the answer is quite often determined within the first 5 turns of any game (starting civ + starting area).
Ideologies are simply just expanded versions of what were originally the three lategame policy branches; since cultural victories are not earned through policies, ideologies simply are a way to accelerate a culturally advanced player along any of the victory tracks. Much like with regular policies, you can often determine what ideology you want to go for and what tenets to snatch up first long before they are even unlocked.
Given how murky the diplomacy system is (there's little functional middle ground between "this civ hates me" and "this civ likes me") and how the AI does not actually attempt to bribe other AIs to pass resolutions, the World Congress just becomes a random bonus/penalty generator in singleplayer. Now if AIs actually attempted to pass resolutions they know other AIs would agree on and would vote against players if they know their vote for a player would never win, that would add depth to the diplomacy system (it's why I've implemented the latter into the next version of my mod).
- and yes i lost a battleship to a spearman back in the day
