If we're talking some wish-list items, I think the stuff that I would want most (I mean, not really "most", but like "stuff that I think had potential but could use a good amount of re-work):
-Make Appeal Great Again. Honestly, I find the appeal mini-system is a lot of fun. In theory. But like, it's just hardly used at all. A couple of civs have some good ways to interact with it, but other than that, it just doesn't work for me. Never mind that the whole "neighbourhoods get more housing from appeal" is one of those items that sounds great in theory, but when you actually dig into it, you're better to put a neighbourhood in the middle of the tundra because trees and coastlines, rather than right next to your city centre/industrial zone.
-Make more parts of the game change as you go through. I think one of the missing aspects is the sort of lack opportunity cost decisions. If you place a +5 campus early, it's more or less still a +5 campus late. Like, it would be cool if you could find a balance in the system where, say, a campus has +1 adjacency per mountain in the early eras, but in the later eras, its adjacency shifts to the reef/geotherm/rainforest. So if you place a +3 campus early because it's near a bunch of mountains, that's great, but long term it's not going to be as good as another one.
-Give you more decisions on shaping your empire. Another awesome early "mini-game" is the Pantheon rush. It's like, how much do you have to rush to get your top choice, before it's gone. Religion is similar - who can found the first religion and get their top pick. Other than that, I mean you have the usual wonder rushes, but you just don't have the options. I know people have mentioned the events system above - honestly, I would love to expand that out more. Like, it would be really awesome if you have a volcano go off in your territory early in the game and you are given a popup decision - "Your people are worried that you have angered their Gods", and you get 2 choices. Maybe one choice is like "we will declare that area off-limits", you gain +1 faith per volcanic soil tile, but you cannot build cities or districts on volcanic soil. Or if you choose to ignore the pleas, maybe you get -1 amenity for each district or city placed on volcanic soil. I dunno, give me more ways to choose! Or even like sometime early in the game, you have to make a choice of how you want your empire to grow - do you want to focus on farming or fishing? If you focus on farming you get +1 food per farm. If you focus on fishing you unlock Fisheries as a tile improvement.
-Reduce the late-game micromanagement. I know some people we talking about builders above, and for me, I both love and hate builders. Early game, I think they give you some real opportunity cost, and I think it makes a lot of sense. But once you get to the mid-game, they're just a pain. I'm basically just going to spend X gold for a builder with Y charges, who will go and spend those charges. It just feels needlessly complicated. Even if they just changed it so that once you got to Civil Engineering, you could simply buy tile improvements with gold from the map directly, that would be oh so much better. Similarly with city management late. Early on I really do want to micro-manage things. But later on, I wish I could just pin the districts I want on the map, and let my cities just manage themselves. Governors too - early on it can make all the difference in the world. But once I get to the mid to late game, it's a lot more "set it and forget it". Honestly sometimes I get a governor kicked out of my city and it takes me 15 turns to remember to put them back, because I just don't care. It really feels like once you get to the mid-game, I wish I could just like draw some lines on the map, and be like "here is a 'state' of my empire, and you just assign the governors to the states with a generic bonus, rather than city by city. So maybe Pingala as a state governor gives you +10% science and culture to all cities in the state, rather than the larger bonus for just the one city.
-Simplify the systems. I don't mind it, but I can see it being hard for newer people. Having a diplo favor counter, an envoy counter, free envoys at some places in the culture tree, free governor titles, free spy titles, etc... I kind of wouldn't mind if virtually all those system just fed into one. So when the bucket rolls over, you choose if you want a free envoy, if you want a governor title, if you want another spy slot, etc...You'd have to rebalance them, but I think that would also give you another decision. If you want the governor titles, you won't be as high in relations with city-states. Or if you want to focus on espionage, you have to give up another part of your empire.
Anyways, just a few items that are on my personal wish-list for the 1/3 of the game that I think could be "changed" for the better.