Science will increase district cost, not in general, but it just will. And in the early eras before we get Apprenticeship, science is not going to do anything for production. Yes, it sounds beneficial to get Apprenticeship and Machinery asap, but at that stage of the game, these factors make me delay those Campuses:
- I want those Settlers out there building new cities.
- I want those Entertainment Complexes to keep expanding.
- I need those Builders to improve the land so my cities can grow to build those districts.
- I need those Commercial Hubs so I have money to buy better tiles for my citizens, and the internal trade routes from the Trader matches my goals for this stage of the game.
- I want the Industrial Zone asap (else what's the point of virtually bee-lining Apprenticeship?) at minimized cost, so the IZ is usually my third district for core cities and the first district for my newer cities.
- A neighbor or two is having funky ideas and I may be distracted for a while churning out those Archers to fight off their horde of warriors.
- Machinery is only going to help individual cities that have access to forests, and often I will also need food tiles to support those lumber mills (we're not always blessed with grassland forests everywhere), meaning I need the pop, the entertainment, the housing, etc. And it's easy enough (with Eureka moments) to get Machinery without any Campuses.
- Having Campuses up first at pop 1-7 means my district costs inflate at a faster rate for a longer time than if I build those Campuses at pop 10.
It just happens that by
not prioritizing science, everything lines up so well. Yes I could rush those Campuses and get all the tech unlocked, but I'm not going to have the population to build those districts I want, so I end up letting the cost inflate continually because my Campuses are still pumping out that science, and the increases in production due to science (Apprenticeship +1 to mines/quarries, Lumber Mills, even Factories) are not going to double my production to offset enough of the cost inflation.
I believe most players have tried their first game or so focusing on science and built all those sweet Campuses. I did exactly that in my first game, and districts became expensive as hell. Then when it was found from the code that district costs scale on the number of techs/civics researched, we all
experimented delaying science, and the result was much more favorable than when we focused on science.
So in the end it's about lining up the acquisition of Apprenticeship with the growth of your empire so that the moment you get Apprenticeship, you can lock down those IZs in more of your cities, while not gimping your empire growth in the mean time by not expanding due to not wanting to use up the allowance for an Entertainment Complex or gimping the economy because you built Campuses instead of Commercial Hubs and Traders. As I said, it's not purely that +3 hammers is better than +4 science, but that the +4 science didn't help me as much as I thought it would.
I may try another game prioritizing those Campuses, seeing how I understand the game much better now, but I really doubt it will turn out better.