Like, if your saying encampments are a bad investment. Are you comparing it to theatres and holy sites? I hardly bother with research centers even. Why are these better?
Someone in another post asked for a list, but I can't really do that because so much is situational.
Holy Sites are weird because if I'm going for a religious victory, they're #1 priority, both in terms of build order and quantity. otoh, if I'm going for any other VC, I frequently build none, and acquire a few by conquest.
Theater Squares are similar to Holy Sites, but not as extreme. If I'm going for a Cultural VC I build a lot of them (although I hadn't thought of Victoria's Trump-like resort strategy - I may have to try that now

), and even when I'm not going for a culture victory I usually build a few so I can get new Civics fairly quickly. One big use for getting new Civics fast is to have good agility in switching policies. I'll often skip Civics I don't need right away, just so I can have a 1 or 2-turn Civic ready to research later. For example, I'll adopt Professional Army, upgrade all of my units while I research a 1-turn Civic, then replace Professional Army without paying the fee.
Campuses are similar to Theater Squares, although slightly more important because keeping my army on the cutting edge is key to my ability to win wars (and I
think it's important to maintaining a deterrent and to getting the diplomacy modifiers from Civs that admire strong militaries, however I'm not positive what the relationship is between an army's weapons and its size in these instances). So I'll build more than a few Campuses, regardless of my ultimate goal, and if I'm going for a Science Victory then they jump to #1.
I would say that Commercial Districts are my #1 district, only falling to #2 if I'm going for a religious victory (which I rarely do). Harbors are vital for a small number of cities. Conversely, Neighborhoods are ubiquitous, but come so late in the game they're rarely of great impact.
Industrial Zones and Entertainment Complexes are both important for every city, to varying degrees. Luxuries are fungible, so if City-A has an Amenities shortage, sometimes the solution is to build an Entertainment Complex in City-B, even before you unlock Zoos. The usefulness of Industrial Zones has a lot to do with the map (Encampments don't get Adjacency Bonuses) and how close your cities are to one another. I prefer to spread out as much as I can, but sometimes that isn't very much.
Holy Sites in non-religious games, Space Ports in non-Mars games, Aqueducts and Aerodromes all rate behind Encampments, in my view. A friend of mine insists that I'm undervaluing Holy Sites in non-religion-VC games, but so far I'm not seeing it.
And of course I've been talking about Districts this entire time, but really, the value of
anything I could build needs to be compared to the value of
everything I could be building at that same moment, for however many turns each of them will take to build (someone mentioned earlier the Social Policy that reduces the cost of Encampments).
At any rate... nobody is building these things in order to win. There are a number of reasons to build them, but simply to win is not one of them. The only way to lose in VI is the early zerg, and unless you get a hyper unlucky start, just building 2 warriors and a ranged bang-bang-bang will insure your survival.
That's an important distinction. I was taking the 'value' of Encampments to mean "how much they improve my chances of winning, compared to everything else." I agree with you, the only time I get killed on the battlefield is the early rush, when I couldn't have built an Encampment yet anyway. So unless someone wants to mount a defense of the AI's warfighting abilities, I think the value of Encampments is solely in their non-military benefits and applications.
This point of yours ties neatly into something I was thinking about just this morning: If Encampments are indeed just as useful as other, commonly-used districts, does that mean they would be OP and in need of rebalancing should the AI ever get a dramatic makeover in its warfighting? I would think that, for the Encampment supporters, the answer must be 'yes', but maybe there's something I haven't thought of.