I'm gonna be honest. Why would I waste a district slot on encampments?
Even if I get declared war upon out of nothing (highly unlikely, I tend to have DoFs with most if not all AIs, and if not there's a good chance I'll have my suspicions about an AI already), I can build up a sufficient army to defend myself before the AI can take my city. Just gotta build a bunch of ranged units, station them in cities or on defensive terrain, and maybe a few melee units (or, if vs'ing cavalry, anti-cav) to defend everything.
I can't remember the last time I've lost a city to the AI in a war that wasn't declared in the Ancient Era (if it ever happened...), and frankly, beyond not building encampments I tend to not even build walls. Again, unless attacked.
Honestly, I build encampments in two situations:
-Because it looks nice as a defensive fortification, e.g. blocking off a mountain pass.
-Because I'm going for a conquest victory and didn't forget that you need encampments for Great Generals. (I've played conquest victories without encampments where I did forget this...)
Are you like, playing a different game?
As others said - I'd like to see some screenshots. Because I have no clue how this would happen. Booting up Civ VI right now, here's about what I usually see in a late game on Deity (taken from the last end-of-game save I have, which is like a year old or something) - note that I specifically went for the AI with the highest military score, and revealed the entire map so nothing could hide in fog:
View attachment 699124
Sorry, I don't have any screenshots saved. And I won't be playing civ any time soon.