That's reductive. Balancing is possible in principle.
I would disagree. I hold that even in principle balancing a complex dynamic system is simply not a possibility if you wish to retain either of those properties to a degree that would maintain fun as an objective.
Starting with complexity. As you your self said, game options matter a lot. So does singleplayer vs multiplayer. But that's just the tip of the proverbial iceberg.
Games, especially complex ones like CIV are inherently going to have a lot of emergent properties that are uncountable for. That is to say mechanics that through their interaction create new and unpredictable mechanics that players discover and you as the developer didn't even know existed. Multiple mechanics might each be perfectly "balanced" internally but together they might allow for new and unconventional strategies that are massively "overpowered".
And than we have the random chance factor both in terms of RNG and just good or bad luck for a player. How do you balance a game around someone popping 3 techs in a row from consecutive goodie huts or loosing their one and only starting warrior to a bear and having to delay everything while they build a new one potentially getting killed by barbarians in the process?
And than you have the players. Players are also a huge unbalancing factor. Remember, humans don't always play optimally. Nor are they predictable like the AI. Different people have different levels of skill, temperament and mood and indeed they might want different experiences out of your game. All of which are valid, but how do you balance around them clashing? How do you balance the situation when you have say a hardcore play to win player with low skill coming up against a high skill but casual player that does not care?
The only way to "balance" all of this is thus to reduce complexity to the point where all of these factors don't matter. And as we all know chess where each player only has one pawn is a very balanced game but it's not very fun.
But even if we accept the notion that some sort of complexity based balance can be achieved without completely ruining the fun of the game there still is dynamicism to consider. Which is to say games are systems whose balance changes over time as they are being played. A game of chess might look very balanced before turn one. But once you take a couple pieces it can quickly start snowballing. And in a game like CIV that effect is amplified by the games complexity to a degree where I would argue it is basically unpredictable.
So the best thing you can do with "balance" patching is to constantly play whackamole trying to hammer down what ever is considered the meta this week until your patience or funding runs out.
PS: The above is a general statement and as such there are naturally exceptions. There are indeed situations where a single game piece or mechanic is just badly designed and clearly overpowers others overshadowing them or just breaking the game. Like having a weapon in a shooter game that's both more accurate, powerful and rapid firing than any other combined. But such issues are not issues of game balance but flat out bad game design. Which is to say that the people making that item or mechanics considered it to be good at the time of creation. And as such assuming a competent developer these will be few and far between.