I'm stating the obvious to the point of uselessness here... so allow me to explain further
You use it if you have a good reason to want many GP.
The real question is why would you want many GP as your main strategy?
You can trade them in for tech's to get ahead in the tech race - allowing a smaller defensive army of higher quality units.
OR
You can buld up super specialists in key cities. Picture your super commerce city (many cottages) with high % science, library, university, observatory, academy, oxford university and 5 super scientists. Now imagine it's yor capital and you're running bureacray and representation as well.
EG
Assume 12 population, average of 4 commerce per tile = 50 commerce + 50% for bureacracy = 75 commerce
90% science gives 67 beakers
Add 9 beakers for each super scientist (extra 3 beakers from representaion)
gives 113 beakers. Now add building bonuses - 25%+25%+25%+50%+100%=225%, so total beakers = 367 beakers
... and thats only from a population 12 city.
You sometimes don't need any science buildings in the rest of your empire with this going on.
OR
you're aiming to make as many Great Artists as possible to balance your 3 culture cities for a cultural win.
OR
You're stacking as many Great Merchants into a GP factory city to further boost it's food to make more GP's..... enjoy the positive feedback loop.
Think of it this way : Pacifism vs. Parthanon
- Pacifism can be adopted when YOU need it, and dropped when you don't. Once you've invested 100's of hammers in the Parthanon you can never get them back.
- Noone can take pacifism away from you. There is no race.
- Pacifism doesn't have a huge up front cost in the early classical period when you really need the shields for something else.
- Pacifism gives a bigger bonus than the Parthanon.
Parthanon is loved by many players and I think Pacifism is better
The really interesting question is: "How can I apease, beat off, scheme with other civs to keep an agressive neigbour contained while I progress my GP plan."
The Answer - it depends. Treat every war as unwanted. Plan for it and make it as short as possible. Plan for it even if you didn't start it. Have friends... goos friends and many of them. Make your military high quality (many promotions). Defend well. Make them pay the full attrition bill for starting a war. have commece cities near the core, so the sow growing cottages / villages / towns don't get pillaged. GP factories on the outside are easy to rebuild (farms are quick to make with workers - towns take forever). The benefit to an empire of a GP factory gets exported to core cities, whereas the benefit of a commerce city (the cottages) and a production city (many infrastructure buildings) are not portable - so temporarily giving ground and loosing a GP factory is not the end of the world. Use choke points. Use yor navy if it's a watery world. Use pairs of combined arms fortified woodsman 2 or guerilla 2 defenders on border forest hilltops - the AI will go crazy trying to keep its rear safe as it storms deeper into your empire, and the attrition killing these disposable foxhole strongpoints will really hurt the enemy. If you plan never to need to assault an enemy city tem a smaller military can be used much more effectively.
The ultimate GP focussed strategy looks like this:
Philosophical leader
Parthanon if you're lucky
Representaion
Caste system (if you want to make artists, merchats or engineers)
mercantilism
a reasonable sized empire - lets say 10 cities on a normal map.
2 production cites to make enough military to survive
2-4 commerce cities to keep the economy and Science rolling
4-6 GP factory maximum food cities
A focus for your GP's. Which ones do you want, why, and how will they give you a route to victory?
Lets say you want a spaceship victory
Early on you make super scientists in one of the commerce cities and make it a super science city with Oxford Uni. Mid game you drop great engineers in your best production city, and put the iron works in it.
Let game you use Great Scientists to rush techs. You aim for a tech lead through the modern age, with enough production cities to build the SS. If you need more productrion use your redundant workers to change all the farms to workshops / watermills in some GP cities and build the cheaper SS parts. If it's still a close race then spam a Great Engineer and use it to rush the Space Elevator.
I'm not saying this is the best GP strategy - just the one that uses as many game mechanics that focus on GP's as possible. It may be TOO focuses for some situations