Ya know, just yesterday I was thinking "finally, city specialization exists" and related to this topic. I agree with the guy that said you are trying to just build everything everywhere. Between the district cap and spreading out tech progress (not only splitting science/culture trees, but eureka bonuses, city-states, wide play not being heavily nerfed, etc.), it seems pretty obvious to me that it is by design you aren't supposed to build everything everywhere unless it is a super late game super large city (which you won't have for most of the game).
If I had to label a problem, it would be the exact opposite: I'm looking at a lot of my cities and thinking "Do I need this entertainment district? Hmm... not really. How about culture? Well I already have a lot. Science? I have a lot of that as well." It isn't that I never want to build anything in most of my cities, it is just that it has never been needed to have everything at once, which is exactly my point. Build up your empire by spreading this districts throughout your cities and add more over time, rather than trying to build everything instantly as they unlock.