Need to disagree further.
Courthouses are bad.
1. 4pop is a huge investment. Arguing that they're "only" 3-pop or less is simply the wrong approach. During the time at which you can whip that Courthouse, you actively need to sacrifice research to get it, there's no way around it. You either sacrifice Wealth or you sacrifice population, both is research effectively. Research is, what gets you Cuirrassiers earlier, and even if they only cost 3-pop due to whichever mechanic, once Cuirrassiers are there, 3pop can be a Cuirrassier, and a Cuirrassier is again more valuable. Also you forget, that not all mechanics speak in favour of the Courthouse. While a Courthouse gives benefit while just being there, so while a Courthouse gets increasingly more valuable with time, the

put into Wealth are actually available instant, so already before the Courthouse exists. Also, once Cuirrassiers are reached, cities get whipped to a minimum of population, diminishing the effect of the Courthouse.
2. Doing less is doing more when it comes to buildings. We don't want to build fancy cities that have nice infrastructure, we want a maximum strength army in minimum possible time. While you build all those buildings that pay back by your calculation, that a build is then justifyable, if it produces more of x 'til the end of the game, what happens is, that you attack the 1st target later. This gets you additional cities later, this makes you get additional troops later. In the end, you need longer to proceed towards the next target, and because your opponents will be higher developed, you'll have greater difficulties in war aswell. All of this works against the fastest possible time at which victory can be achieved.
Remember what I wrote about that cycle (edit: was a different thread iirc, ment is the cycle of taking one city after the other and whipping reinforcements from the population of that city and because one city unlocks the ability to conquer the next one, in the end the game is won) , you need to get into that cycle, once you're in it, you've effectively won the game. If at all, a building needs to pay back before it's possible to enter that cycle by gaining enough power, and from then on, the speedlimit is the movement of troops.
Also: Once one is in that cycle, one gets the gold from conquering cities. The additional resources from conquering cities and from having more cities are multiple times higher than anything a non-World-Wonder could offer. Even World-Wonders very seldomly can compete against additional cities.
3. The argument with food-heavy cities not being able to generate a lot of Wealth but otoh being able to whip a lot of buildings is invalidated by the fact, that

can also be converted to

(via Specialists) , and the question is not Wealth or Whip but Research / Units or is there anything, that allows for more of either before the 1st war. Believe me, I have no personal problem with Courthouses, it's just that to me, they're like Markets are compared to Libraries. A Market is expensive and provides mostly nothing on Deity, because in most times it's possible to trade for a lot of

, making

only a factor in that kind, that trading for it means pushing the AIs. A Library though is cheap, and not only gives a greater bonus, but it also gives what is actually valuable = power to develop faster = reach techs earlier = attack earlier + have an easier time selling techs = getting more

earlier = again teching faster + the push on the AIs by trading gets smaller, because one can sell them older and smaller techs.
This is not ment aggressively. I just had that discussion multiple times already. If you aren't convinced, try to think about this: A Corporations-Spacerace is the ideal situation for Courthouse, because long game and no chance to get around Courthouses. And what do you think when HoFers build them? Right before the Executive reaches the city. With ORG, it's a different situation, but without, Courthouses are just too expensive for the little benefit that they effectively provide.