why are large cities detrimental? population gives you more tiles to work, gives you culture, science or gold depending on your governor, gives you flexibility (going full prod, going hard growth, going full specialists..), allows you to exceed district limit. what exactly are the downsides?
also, your assesment that each victory only needs 1 district is simply wrong. campus for example needs campus and space port to even be able to finish the game, but also heavily needs cultural sites because SV requires adequate culture per turn.
CV needs cultural sites and holy sites (for rockbands etc.), one could even argue it wants districts for amenities and appeal. also, I actually do not build my "victory district" in every city, and I don't think it's optimal to build a +0 district in an expansion just because it correlates to your VC. building a harbor or EZ for the additional TR would probably be more optimal in that situation, especially as number of cities increases.
After size 10, it turns out that the benefits of a higher population do not outweigh the costs (this is due to things like specialists being really weak in Civ 6). The cost of housing improvements and districts (like Aqueducts and Neighborhoods) and Amenities are significant. Also, since you only need 2 or 3 District slots, those extra slots don't provide much benefit. Again, it is better to have more small cities, because you can actually get a ton of low-maintenance population that way, and you get more space for your victory District. Yeah, obviously, you need other Districts too. I'd say adjacency is one of the weaker aspects of your Districts. I'm not advocating building +0 Districts, but as long as you can get +3, that's all you really need. A bigger factor is your Great Person generation.
Maybe a better way to say it is not that "you build more cities so you can build more victory Districts" but that "you build more cities to build more of every District." The more cities you have, the more likely you'll be able to find good spots for all your District types and meet the conditions for more Wonders. Districts are the main source of things like Culture, Science, Gold, Trade Routes, etc. etc. So you have to build more of them, so you have to build more cities.
Spaceport doesn't really count as a District in my book. By the time you can build Spaceports, the game is generally won, and you are swimming in District slots. That the Spaceport happens to take a District slot is incidental and doesn't have much impact on the game. A better argument vis-a-vis Science Victories would be Industrial Zones. 3-4 good Theater Squares paired with the right Wonders can rocket you through the Culture tree pretty fast, which is definitely important for SV .
I'd say with the advent of Rock Bands that Faith is more important to a Cultural Victory now, but I don't think every Cultural civ or game should involve rushing to get a Religion right away, and I think Theater Squares would be a higher priority. I usually advocate new or struggling players to avoid Religion, as it is easy to bog down your early game expansion rushing Religion, and it is difficult to realize the benefits without knowing how to capitalize on high Faith properly.
Here's the thing. When I have 15+ cities, I probably have 4-5 +3 adjacency options for my victory District that I can build right away. I also have 4-5 +3 spots for
other District types as well. Yeah, I am not building my victory District in every city (at least not right away), but I can get started on all of those Districts (victory or otherwise) right away instead of waiting for my pop to grow. Why choose when I can build both?
The other advantage of going wide is the same advantage that it has always had in Civ - more building queues and crowding out your opponents. One more city built by you (strategically placed) is one less city built by your neighbor. One of the biggest reasons the jump from King to Emperor is so difficult is because
that's when all the AIs get an additional Settler.
The only reason to build Entertainment Complexes is to enable building the Colosseum. Generally, once I've built the Colosseum, I never have to worry about Amenities again. Even if I don't snag it, I don't tend to build many Entertainment Complexes. Well, unless I'm playing a Civ like Scotland!
I have a secret crush on Harbors, to be honest. I do like playing naval/coastal games, so the weakness of naval strategies throughout Civ 6's history has made me sad. The best part about harbors is they give me something really strong (additional Trade Route) in exchange for something fairly weak (a coastal tile). My favorite part of the District system is how you can use it to make terrible tiles start working for you.
I'm going to sum up my playstyle:
1. Expansion and Defense. Build/capture 10+ cities by about turn 80-100. District costs are locked in as early as possible but I don't build them yet. Focus is on military and Settlers.
2. Consolidation. Focus is on Builders (pumped up by Serfdom and often the Pyramids), any early Wonders I'm aiming for, and chopping out the Districts I locked in earlier.
3. Victory. Now the game is pretty much won, so I settle down for 100 clicks of the End turn button while managing my Empire,and keeping track of my rank in my Victory area (e.g. am I first in Science? Am I first in Science generation?)