I barely built them before, I build them even less now. Its always a district that I will use mainly for defense purposes/housing in the first half of the game, era score/housing in the second half.
First half to make a narrow pass defendable without units, or very few of them, or kind of in the middle of a cluster of cities for defensive purposes, or on the borders against a violent neighbor if he/she is doing advances. Also to get some more housing if its unavailable from other sources, and if there is nothing else but units and wonders I dont want/need to build.
Second half will be mostly just for the eurekas and era score, as the army Ive built in ancient/classical is almost all alive, and will most likely just need an update, or buy cheap lvl1 units tomerge with the experienced lvl 3 and 4s, to create some nice corps and armies. Build a couple more units perhaps to complete the army with units of all kinds, you know, just to be sure theres variety and a counter ready.
If Im going ultra-warmonger, Ill never build encampments in cities I have conquered. By the time I could build anything I could make use of, my troops are healed and they can continue pushing.
If I build them, I will have 2 if the lands I settled are decent enough, more if I need housing early in the game and I cant build aqueducts or farms.
One with barracks and one with stables.
In any case, due to my mostly peaceful playstile, the encampent is usually the 3rd district I unlock.
And by that time I have settled a couple or 3 cities. If I need to complete my army, Im switching cards and building one or 2 units in each city. Its faster than building them in a single city and they can defend their respective cities immediately instead of needing to travel to another spot. Just build the cheapest units in the smallest cities and the only thing you dont get is the bonus exp, but at the beginning of the game, having more units sooner is more important than having higher quality units, in my experience.
Last game with Shaka I built quite a lot of them, roleplayer as I am, they are cheap to build yes, but this delayed my usual turn count by about 80 turns(epic speed). The production bonus they give is laughable compared to how much it costs in time/gold to fully upgrade one.