A city generates a great person when its OWN GPP reaches the current need. That means: if a great person needs 2000 GPP now, and a city is running 3 specialists and generating 9 GPP, it would never gather enough GPP to create a GP, therefore the 9 GPP is simply wasted. So it seems good to run only 1 specialist farm, and let other cities concentrating on production.
You forget that your civ, one early wonder (which one escaped me at the moment) and a civic choice (pacifism) can severely reduce the amount of GPP to produce a leader. Certain wonders add GPP as well. I think that you can run 2-3 of these cities (out of ~12 in the early middle ages).
I think if you have lots of rice/ corn/ pigs/ flood plains in your empire half of these food rich cities can specialise in specialists , the other half in commerce (lots of towns).
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