hmmm, at chapter 16 the pop is 214 per square vs 650 for a magic building (excluding warm springs bonus pop)
I do not really need culture, so I guess it depends if you can make use of the culture bonus.
I personally already have enough (event) culture buildings in my city So I do not see much use for it in my case.
Guess it's a nice building if you started playing in the past 12 months or so.
Your math is incomplete
Unlike Frank you don't have 100% Magic residences- in fact you have 28 regular ones giving you
341 pop/sq
vs
190 pop/sq in the hut
Then we have your armories that make
1730 orcs per 12h
vs
1750 orcs per 24h in the hut
That's basically half of an armory.
Your armories each take up 28 squares, plus 2 roads, plus 24 squares of pop, plus whatever the supplies cost to run them is(let's say zero)
I see you also have Grounds of the Orc Strategists in your city, each taking up 9 squares and producing
760*2pop= 1,520 units per day
vs
1,360*4pop=5440 units per day
------------------------------------
So, even if you value the 16,000 culture at zero, and the supplies saved in orc production as worthless, the Witch hut for your particular city gives a space value of
10 sq of residence population
27 sq of armories orc production
32 sq of grounds of the orc strategists
--
69(nice) squares of value, and only needs 18 squares of space.
You could even value the population and orc production at
zero and it's still worth placing in your city because it takes up the exact same space as 2 of your Grounds of the Orc Strategist while producing more than 3.5x the units.