TheMeInTeam,
This type of stuff bothers me. If I find an awesome city spot for a GP farm, I'm going to make one. If I can find two spots, I'm going to make a 2nd one. If my empire is large enough to support it, I'll make a 3rd. Why? Because I'll get Great Persons faster. As primaraly a SE player, I find that GP farms often become psuedo science cities, as well. Furthering how useful said city is to my empire.
Also, I hate hanging onto Great Persons. I find it inefficient. And the more GP farms I have, the more I can specialize each GP farm. And done properly, I can hold off getting a GS from GP farm #1 and get myself a GM from GP farm #3 so I can make Sid's Sushi, rather than relying on random numbers.
I find it more efficient to have control over which GP you will spawn. And don't give me this caste system talk. I like to run Slavery for the entire duration of the game.
There's nothing wrong with making more specialist cities if you have the food. By all means, do it.
However, the most efficient use of GPP comes from 1 city or something odd that I don't remember like every singe city being identical or something.
Too often, the GP farm city creates specialists at such a rate that it laps the other city, so that the other city is never the one to cross the threshold of GP generation.
First GP needs 100, then the next one 200 etc. Even if the 2nd city is at 99 though, it will now need to make 200 after the first GP is made.
Yes, you can hold off one vs the other. I, like you, prefer slavery however, and in many cases this limits what GPP can be generated based strictly on slot limits. You can't keep merchants/prophets/GE's very pure in the early game or all you'll get is scientists from a scientist farm.
You mention slowing one down vs the other, but at some point this will slow down GPP generation enough that 1 city could match all 3, especially if someone is running NE/Great library for example. The NE makes it so that one city has double the GPP of all other cities all things being equal (or with pacifism, which is a situational civic IMO, 3/2). This city will tend to overwhelm other GP farms unless you curtail it, but then you're hardly getting them "faster".
Gliese made a good point about the distinction of pre vs post NE GP farms. Early in the game though I always viewed it less as "here's a GP farm" and more like "I want early scientists or a priest so I'm running some specialists where I can to get it". It's hard to get a spectacular GPP pool, ESPECIALLY a pure one, pre NE anyway.