I don't have any problem with them early (turns 1-3 or 1-4), but in the late game they just sort of drop in the game and since you've already specialized they feel like random points to a lucky player.
i think the objective cards greatest strength is their greatest weakness. You need to score at least some of them (usually most of them) to get a decent score, so they push you in a certain direction. This is fine when you're new to the game but later it is a creative blocker. If i decide that this game i want to specialise in democracy and trade but then all the cards i get push me toward different things i have to choose between playing the game how i want and probably losing and playing the game how the game tells me and getting more points. I personally would like to see an expansion for the game deal with this. I like the idea of having some cards that get you extra points, but perhaps you could draft them or something to give you some more player agency over your score.
I can certainly agree how in the late game you have very little ability to shift directions based on being dealt Objectives.
I'd also say that some of them are just substantially easier than others. Stuff like the "Wood!" objective are trivial to accomplish regardless of what anyone else is doing. "Build the most X" can be harder if someone else has the same idea, even without the objective.
I find the Objective cards to be way too gamey. "Collect 5 Stone" Why? To gain 2 VP? Okay, but what is this doing? Why am I doing this for my civilization? "Build 2 boats". I don't care about boats, why build them? Because it gives me 2 VP. This isn't civilization building, this is just nonsense. As has been pointed out, you can't just ignore them, but a lot of them are dumb crap that tries to steer you in a direction. It's like the game doesn't think there's enough motivation to build a civilization, so it threw in these cards to make it more appealing or something.
I just noticed the expansion is adding horses and elephants so yay, more combat.
You can trade those Objective Cards. A lot of the time a player already has something that would complete one of your objectives, and if that objective isn't doing you any favors you might be able to swing a good trade.
I still don't get the ire around the military/combat aspect of the game. Military conflict belongs in a civ game and it should be a big part of the game. Most civilizations have waged or faced military conflict. CoC gives you quite a few ways to deal with it. If the military aspect of the game really bothers you that much why not just play something else? There are lots of engine-building games out there with varying degrees of interaction. While CoC does have some engine-building to the way the techs interact it's still a civ game first and foremost.
I disagree that a civ game is essentially just a themed wargame. I realize that war is a crucial part of history, but history is more than just the history of war. I want to found and develop a civilization, not work my way from spear to nuke and every now and then harvest grain too.
But yeah, it sounds like CoC is not interested in that.
Would you say Nations fills that niche now that you've been playing it right? Civ games are one of my favorite genres... I wouldn't mind having a less aggressive one. And I seem to enjoy tableau games, I've gotten into my vassal games of Pax Porfiriana.
I must admit I never remember I can trade cards. The resources part seems natural but I forget about objectives.
I think that CoC does a good job balancing the military aspect. While it is true that history is more than just the history of war, if a neighboring country becomes aggressive, it really does force surrounding countries to respond in a like manner (or risk being overtaken).
Unfortunately, I think that military conquest is a very large part of civilization building (either offensive or defensive). The uniqueness of civilization games is being able to create an "engine-building" game in the context of military aggression by others.
I also agree about the Objective cards -- use them as barter. I think that is some of the interesting part of the game as well; being able to balance your vision of what you want your civilization to be with the rewards of the objective cards. I always view the objective cards as the demands of the citizenry.
I wonder how many leaders throughout history have been frustrated because all they want to do is develop their civilization to be the best it can be, but instead they have to deal with some militaristic asshole. I'm guessing its a pretty high number. So I think any civ game worth playing should have that built into it in some way. Maybe the trick you're looking for is to not have that threat come from the other players. Sort of how the barbarians attack in Cities & Knights where, iirc, there's a set amount of defenses to build then you can move on. They don't keep building up on your border forcing you to keep building more defenses like another player would.