Courthouses seem to be a typical CIV V 'one size fits all solution' that just doesn't fit anything. It's too expensive in the early game, too cheap in the late game, is the same solution for any and every city, and provides such a burden on the economy that people would rather raze a city and resettle it.
What I suggest is a culture based conversion of the city. The amount of culture needed would be related to the number of hexes in the city catchment. This would make a former capital much more difficult to convert than a newly built one size city, which it isn't at the moment. All culture earnt by the city until it is converted would not expand the city borders (as it does presently, as if the city was newly built) and would instead contribute to the conversion only.
The courthouse could then become a building which helps speed the conversion of the city, perhaps cutting the amount of culture needed by 50% and adding +2 culture/turn. The courthouse replaces a monument and they cannot both be built in one city. I would also stop culture from the city counting towards policies and cut income, trade routes, and research from the city by 50% until a courthouse is built. I don't think the current courthouse cost justifies this so I would cut the cost down to be appropriate for the mediaeval era. Whilst this would make a courthouse cheap for the modern era, a courthouse alone will not be able to convert a mature cultural city.
I would even go further and suggest that the former owner of a nation should still be able to use the roads of the city in wartime since the population sympathises with them. A courthouse or full conversion would prevent this.
What I suggest is a culture based conversion of the city. The amount of culture needed would be related to the number of hexes in the city catchment. This would make a former capital much more difficult to convert than a newly built one size city, which it isn't at the moment. All culture earnt by the city until it is converted would not expand the city borders (as it does presently, as if the city was newly built) and would instead contribute to the conversion only.
The courthouse could then become a building which helps speed the conversion of the city, perhaps cutting the amount of culture needed by 50% and adding +2 culture/turn. The courthouse replaces a monument and they cannot both be built in one city. I would also stop culture from the city counting towards policies and cut income, trade routes, and research from the city by 50% until a courthouse is built. I don't think the current courthouse cost justifies this so I would cut the cost down to be appropriate for the mediaeval era. Whilst this would make a courthouse cheap for the modern era, a courthouse alone will not be able to convert a mature cultural city.
I would even go further and suggest that the former owner of a nation should still be able to use the roads of the city in wartime since the population sympathises with them. A courthouse or full conversion would prevent this.
