Those articles really need to get taken down, as many people get a little confused by it, I see. I was too when I started playing, and then couldn't figure out how to actually use SE, because early on you can only have two scientists, and the economy will basically crash.
A hybrid approach is far superior.
You specialise some cities, but most are hybrid; ie, they have both
and
Capital: Cottages
Great People farm: Lots of food, farms, and buildings that open up more specialist slots. Run max specialists (including starving the city, but not so much it loses pop) during Golden Ages, with Caste System and Pacifism
Heroic Epic city: Lots of hammers, but also decent food so it can grow big. Later on you build workshops for more hammers. Produce military units non-stop
Those are really the only three cities you need to specialise. Everything else depends on what you want for the given map. More GP farms isn't a bad idea, and you may want a good food city to be specialised too, and build the Globe Theatre there, and whip and draft non-stop, because then happiness/whip/draft-anger doesn't matter.
If the game lasts long enough, you can start to transition into a hammer economy, where you build lots of workshops. You can also mix in watermills and windmills for more commerce.
It can also be a good idea to have some more commerce cities, where you basically spam cottages. If you have a city with some floodplains and normal food on top, this is a good candidate.
Oh yes, one more city you can specialise in the late game, is a National Park city. For this, you want many forests and/or jungles around it. Build forest preserves on all these spots, and build the National Park wonder in it. Then you get a free specialist for each forest preserve that is in the city's big fat cross. Sometimes you can get something like 15 free specialists in a city like this, which is great for late game golden ages.