I do think they can add more complexity in other areas hough.
It has been a joke since the original that dealing with the computer is like trying to barter with a schizophrenic, and sadly newer versions have only gotten a little better. AI's will still go from "I love you and want research agreements and luxury trades" to "I denounce you" and verge on war in the space of a turn.
Notably, the addition of the City-States was a big improvement, as they mostly respond logically, and their trend over time is to stabilize back to zero. They also provide you clearer guides on their emotional state and what actions will +/- it. If the main AI players were closer in the information they provided, and the options you had for interacting with them (ie, you could do things like destroy barbarians near them or gift them back their workers to increase your friendship) then the main AI might actually be reasonable to play with diplomatically.
It's controversial, but not without its benefits. Really depends on the type of gameplay you're going for, IMO. I enjoy a very diplomatic game of Civ4, for instance, and I try to squeeze every ounce of quasi-emergent diplomacy and even policy gameplay from what little I feel is there. But I realize I'm in the minority on this. Most Civ gamers seem to prefer a purely military game. In fairness to them, that's the clearest objective of the game. But I like that Civ allows you, albeit with a great deal of against-the-tide effort, to play a different type of game.
I never made the leap to Civ5, due to what I perceived as oversimplification, and a trend away from precisely those features I liked (but which everyone else seems to hate). So I can't really comment there.
It was weird when it came out, that people were lauding a hex map as perfect. In reality it adds very little (given diagonals, it's less freedom of movement). But the strangest thing was... why go for a cell structure at all? In an age where you can calculate real distances, it's a massive throwback. Civ games are about resource management - cell-based maps are not fundamental to this.
Not to mention that they really gouge for the most minor DLC. But llike you, I perceive myself in a minority - Civ 5 is one of the most-played games on Steam.
Would a game of chess be any better if it featured pixel-sized cells and real distances? Some games, especially turn-based, are more fun with a limited number of acceptable actions, because they require you to think in a certain way in order to win. In a game, you may end up weighing complex pros and cons of placing a city between two adjacent cells; that gameplay element would be a lot more hand-wavy with pixel-sized cells.
That said, Rise of Nations might be for you, if that is what you are looking for.
Keep in mind also that chess is an extremely abstract version of combat, whereas Civ is trying to emulate civilisations. Likewise, chess has six different kinds of pieces, all of which play very differently. Civ effectively has three: 'ranged unit', 'melee unit', and 'air unit', without much difference between ranged and melee. There simply isn't the scope for clever arrangement or movement of pieces like in chess - civ combat is more simplistic like checkers... a game which very few people enthuse about.
When we recognize patterns, like, when we throw a ball at a moving target, we don't consciously analyze things, but that doesn't make it "hand-wavy". With a more complex map, it might take longer to develop an "intuition" for it, but that doesn't mean there are not a lot of complex and somewhat precise "calculations" going on, it's just that we're not that aware of all of them.
Again, I'll have to take your word for the annoyance of this element in Civ5. In Civ4, the UN is the closest equivalent. I found it to be somewhat enjoyable, if inconsistent in its decision making. It can throw a real spoilerish element into the gameplay that I like in my games. For instance, if I'm over-relying on my nuclear arsenal as a source of military power, and the UN suddenly bans nukes, the playing field is leveled toward factions with bigger conventional forces and fewer nukes. I have to adjust accordingly, or else pray that the issue comes up again in another UN session and is reversed. I dig that.