Semi-necropost, but whatever...
I don't think it's been brought up yet, but there's one *thing* that made Civ4 superb that's been missing from Civ5 and even more so from CivBE. I definitely know there was some of it Civ3 and a bit less in Civ2, but this *thing* I'm talking about is why I'm really, really hoping that someone other than the current Civ5/CivBE team will head the design of Civ6.
That *thing* is design elegance. Civ4 is filled with it, Civ5 has almost none of it.
Let me give you a few examples of design elegance in Civ4 if you don't know what I'm talking about.
Long post incoming!
First though, a bit of background info: Civ4 dealt with governments by a system called civics. They were essentially government "modes" that were split into 5 categories (government, legal system, labor, economy, religion). You slowly unlocked them via tech and could mix and match any civics you wanted, albeit with a few penalties: 1) each time you swapped civics to a new batch, your empire would go into "anarchy", where you essentially missed a turn, and 2) each civic had an associated upkeep (gold was used to control expansion in Civ4 and happiness was used to control individual city growth) that affected the amount of gold you had to pay each turn for your cities.
First example of design elegance: the "democracy" civics (Universal Suffrage, Free Speech, Emancipation). These civics were supposed to be the more democracy-oriented civics for Government, Legal, and Labor respectively. Their main effects were to boost the yields of Village and Town improvements to ludicrous levels: you could essentially have a Civ5 custom's house's worth of gold yield that generated a hammer as well from a regular improvement. The catch? Well, Village and Town improvements couldn't be built, they had to be grown. Workers would build a Cottage improvement, roughly equivalent to a trading post in Civ5, and when that Cottage tile was worked for 10 turns, it would turn into a Hamlet (with slightly improved yield), then a Village after another 20 turns, then a Town after a final 40; Emancipation cut the time in half, but it was still a very long time.
Here's where the elegance comes in: if an enemy unit pillages a Village/Town tile, that improvement gets destroyed, which means it will take another 70 or so turns before someone running a democracy civic would get their bonuses back. As a result, Civ4 disincentivizes "democracy" players from waging wars, or at least wars that are close to their home turf, because a single wayward enemy unit could wreck untold havoc on a democracy player's economy.
Another example of design elegance: religion civics. Besides the default civics, there are four religion civics in Civ4: Organized Religion, Theocracy, Pacifism, and Free Religion. Organized Religion gives a production boost when producing buildings in cities that have your religion and lets you build missionaries in cities without monasteries (in Civ4, missionaries require a monastery to built in a city before they can be made, which can cost quite a lot of hammers and can no longer be built after Scientific Method is researched), Theocracy gives a barrack's worth of XP to units produced in cities with your religion (and a second effect I'll ignore for now), Free Religion gives +15% beakers in all cities and happiness from each religion in each city, and let's ignore Pacifism for now; Organized Religion has High Upkeep, Theocracy has Medium Upkeep, and Free Religion has Low Upkeep.
The elegance comes from the bonuses themselves. Early on, being able to build missionaries without have to dedicate hammers to a separate building is a huge boon, the +25% production boost to buildings is also quite helpful, and the high upkeep is easy to swallow when you only have two or three cities. Likewise, the barrack's worth of extra XP to military units means all your military units essentially start off with one extra promotion, and the medium upkeep is even easier to pay than Organized Religion's high upkeep. However, as the game goes on, those bonuses start losing their worth: if you already have monasteries built in each city (they give culture and a bit of science, so it's worth building them sooner or later), that missionary bonus is wasted, and the +25% production boost becomes less and less worth the ludicrous amount of gold you'll have to start paying in upkeep. Similarly, Theocracy's XP bonus becomes negligible when you already have two or three XP-giving buildings in your production cities, since the increasing XP requirements to promote a unit at higher levels means that your units aren't starting off with an extra promotion, just an extra 2 battles' worth of XP.
Even if you have all religion civics unlocked, the game incentivizes following a historic route: having an organized religion or theocracy in the ancient and middle ages, and slowly migrating to free religion in the industrial and modern eras. And this happens naturally through just a simple set of static modifiers, not through forced era gating or arbitrary increases in units' cost.
A third example of design elegance: espionage in Civ4. Espionage in Civ4 worked in two halves: you generated espionage "currency" in your empire from buildings, civics, improvements, etc., and you could spend that intrigue currency on espionage actions performed by Spy units. Spy units were essentially civilians that were invisible to all other units except enemy spies and did not require open borders treaties to move in other people's territory, so you could actually use them as scouts as well as for the espionage system (that's a fourth example of design elegance!), but otherwise you'd have to move them into position before you could use them to perform an espionage action, like stealing gold or poisoning a city's water supply or sabotaging a city's production. To counter spies, you had access to both passive and active counterespionage. Passive counterespionage could be done by increasing your own espionage generation or by building buildings, and it increased the espionage costs of actions against your empire, to the point where people would just go mess with someone else because actions against you would be too costly. Active counterespionage could be done by placing your own spies throughout your empire and having them just watch for spies.
Here's the elegance: spies were still units, and just like all units, you had to pay upkeep for them. And since large empires often needed at least 12 or so spies at minimum to perform basic counterespionage duties, that's a lot of upkeep for having to cover so much ground. You essentially had to decide whether to pay a stupid amount of upkeep to keep your empire spy-free, or to allow a few cracks here and there to give yourself some financial respite and hope your opponents wouldn't catch on.
No weird interplay between increasing spy costs and weird intrigue counters on top of cities, just three basic systems meshing together to form this wonderful system: the fact that you need to place spy units in your enemy's empire to activate espionage actions, the fact that your enemy needs to place their own spy units all over their empire to catch your spies, and the fact that each spy the enemy maintains is another unit they have to pay upkeep for.
I could literally go on and on about Civ4's elegant design, and I'm sure I'm not the only one. This is why I'm so worried about Firaxis' current trajectory (Civ4 -> Civ5 -> CivBE). It's not because they're making bad games, it's because they reached a pinnacle of design elegance in Civ4 and then proceeded to replace these elegant interactions with gamey, overbearing, needlessly obtuse systems that often ended up working worse/shallower.