Well placed cottages or well organized specialists allow unlimited expansion. Courthouses in core 6 cities only saves 3ish gpt, and even in 'second captials' you take in a rush you only hit 5-6gpt. It doesn't give you anything that another pop point wouldn't give you better. Workers are better, temples are better, specialist slots from libraries are better, granaries are hands down better...
For builds that are normally around their time markets are better if you're % is low, and generally better long term investments (for % and

) Colosseum are better (1 well placed river cottage gives food and commerce, or you can run another merchant for GPP and commerce) Just plain getting currency is often almost as good as getting a courthouse in every city (if you have trading partners in a small empire) for 0 hammers...
How are they not fairly weak early game? Until you get enough cities that maintenance is over 10gpt they are a waste of hammers. Your core 6 shouldn't fall in that category even on higher levels until your per city maintainence starts racking up (12-20ish cities, depending on level), and you probably need units or workers or just plain settlers more than a few gpt per turn.
Late classical they start looking nice if your expanding and waring a lot, but by then the Zig is just a 33% cheaper courthouse. If you're running a small empire with specialists or going for culture courthouses are never really worthwhile builds unless you get corps...
The only place a Zig is nice is if you're running an EE based on Great Spies, and I do like them in that case.
Island or Fractal maps might be an exception to that though, colonial costs and all.