Im not sure specialization is necessary or efficient in most cities. I mean there's the glaringly obvious GP city with two 6 food resources and little production and the all-too-easy to spot 13 riverside grassland / floodplains bureau capital. But most cities in my games serve multiple purposes for whatever the moment requires. I'll whip commerce cities and farm some of their tiles to prep a rush, I'll whip overflow into Globe Theater in a double food city and just endlessly whip units, I'll use a production city to build wealth and or research, and I'll oscillate a GP farm between GP farming and production given a few decent hammer tiles. Most of what would be considered specialized cities according to this article end up being a hybrid between commerce and production. And many cities that the article considers commerce worthy end up getting farmed for whipping.
Outside of the bureau capital working commerce tiles in the mid game and beyond, the early game turns are the most important and sets up the game. And it is during the early game that I'm switching around worked tiles for all cities and often reprioritizing the city's purpose every few turns.
These older hard - and - fast tips are somewhat antiquated. Though I will say that production spots are never worth trading up for something else. Good production spots should be exploited as much as possible to juice every last hammer out. But when it comes to settling, I take a more simplistic approach. Settle cities with food in the first ring and if you can get any other resources in the first ring, even better. Then adapt the city to whatever the situation presents. If I need commerce, I'll cottage non riverside grassland etc.
I do use this article's technique when determining the best role for my capital on turn 0. But often even my capital ends up a hybrid if it's not an obvious bureau cottage spam or candidate for wonderspam
disclaimer: shaky deity player though consistent on Immortal.