I don't see how your examples lead to "whole game elements are getting lost."
I do indeed call developing a religion, a Great Library strategy, or a swordsman rush a game element.
That CB rushes are dominant doesn't seem wrong to me, but there are alternatives. Warrior rushes should not be one of them.
I'm fine with the warrior only being good for exploration and some barb hunting, but it means it needs an upgrade earlier than the archer needs one. In vanilla swordsman rushes weren't dominant. A major handicap of the strategy is that you don't know in advance whether you will have iron or not. Only for the Iroquois it was the dominant strategy in vanilla.
Now the swordsman suffers from both the resource requirement and the fact that it comes later than the composite bow. That double whammy is a problem. For knights it's the same; they also have a resource requirement and come later.
In a balanced setup different routes should have pros and cons. Between the different types of units this was fine in vanilla. Now, with the inclusion of the composite bow, ranged has most of the pros (no resource needed & early, relatively cheap, good upgrades) while other unit lines have most of the cons (resource dependent, later, and in the case of horses, weak against cities).
It's difficult to replace one stone of a building without touching the rest, and that's what the developers did when they included the composite bow. They acted like cowboy builders.
I fail to get a religion on Immortal with an average civ only when I have some bad luck. I consider that a fair price to pay occasionally on the second-highest level. Most Civ players never have to deal with it - and the game is balanced for them.
Fair enough. I personally took Pottery away from them, because I find it too unbalanced if the AI is already snapping up all the pantheons without me having a chance of competing with them. Handicaps I find okay, but the difference of starting with Pottery or not starting with Pottery for developing a religion I find too big. I rather give them Archery instead.
The GL usually being out of reach on Immortal is a handicap, but hardly a whole game element. A stronger statement would be that many GW's are out of reach on Immortal - again, not because of balance issues, but because you are choosing to play with a serious handicap.
My problem is mainly with the Great Library. The priority the AI puts on that I find problematic, for other wonders I find it fine. For Halicarnassus I find it too low.
My suspicion is that it's actually not a wonder priority, but a tech choice priority. I've noticed that the AI can be very slow with researching Masonry (prerequisite tech for Halicarnassus). More than once I've seen an AI in the Renaissance still not having researched Masonry - they stole it from me with a spy, or they still hadn't improved that marble tile sitting just next to their capital.
A more balanced tech research choice would go a long way preventing the AI beelining the same wonders every single time - also the Mosque of Djenne and Hagia Sophia are invariably gone very early.
It's okay that a player on a stout difficulty level has a lesser chance of claiming wonders and can only go for a few, but the AI can be given a greater variety in its choices.
I'll add the link to the article.
