I thank the Op for doing such a great job.
even if your numbers may (or may not) be innaccurate,
even if I may (or may not) disagree with your conclusion,
I highly appreciated the work on numbers.
As an engineer, I understand numbers well and think they show much.
As such I really hate when people say : it is X much more because every y turns you can whip then produce 2 more pop ..Etc. the information is lost in all the explanation

blush: I know I sometimes write like that, and i always think : what a mess I did !! my apologies, it makes me hate myself)
As an anti-math guy I hate when people come with answers in terms of equations without giving an real exemple with numbers of with tables/charts. (but giving the equation + an exemple is exemplary

)
May the people advocating slavery as an all-out civic answer the OP with corrected tables/ charts ..etc instead of just saying "slavery is more efficient / it use the food boni better / the principle is to whip more than one pop...". If the principle is to use more than one pop, show the table showing how does that improves the hammer production so much. instead of just saying so.
(I won't do the table myself as I am convinced by cfacosta. even if I love to

and I will still whip a lot : as an usefull tool and no more as an all powerfull thing)
Thanks again Cfacosta.
Now I will consider going to cast system when going to an all out war:
most of the times, if I take a 12pop city, out of unrest due to no-fatcross that leaves at least 4people not working even if my happy boni is good enough + without any cultural income. Some other times with 6-12pop cities, even whipping a 4pop building does not permit me to have positive food. This happen when the food tiles are in the outer ring of the fat cross. So I still loose 1 to 3 pop to starvation even if I whipp each turns. (even with eight towns arround the city, if most are on plains, it gives lot of money but not enough food to feed even 6pop).
This force me to whip until reaching 4-5pop to only loose 1-3 starving pop instead of 8-10. Loosing pop to starvation is really ugly : no 30 hammer for sacrifying it.
I am always sad that I had to tranforme a great 12-14pop city in a backward 4-5 pop village due to my inefficiency in claiming the surrounding tiles (some of the times this city becomes uber-great at medium size : 10-15pop due to all the towns, but it needs the food. At small size it is a burden for the empire: either it has very few town to work on, either it works only food).
using 3 such un-working guys as artists would give me growth of the fat cross the next turn !! giving access to the close-by food ressources or grassland-farms-or even to happy-ressources I didn't have before!! only lost 1 pop to starvation !!! great!
(even whipping a theatre or a library or propagate your own religion is not quick enough : it takes respectivelly 4 turns / 5 / 10 turns to grow the fat cross in which you loose at least 4 pop to starvation + more to whipping)