having city-built farms or lumbermills affect tile yields seems even more backwards than the current system, the tiles should already have been improved by the workers.
I'd totally get this comment but I think you missed the origin of concept post. The idea is that the city may build only one of a number of these, giving the player a strategic decision in what way they want to improve their local improvements. Of course, they would require that the city HAS such an improvement already in the city vicinity as well.
Let's take the farm, for example. A city without any planted resources in its vicinity may have the options:
Hay Farms: -1 Food an all Local Farms, Free Support for X# of Units; Requires a Stables,
Hemp Farms: +1 Production on all Local Farms; Requires state access to Hemp, Gives a Hemp Resource.
Cotton Farms: +1 Gold on all Local Farms: Requires state access to Cotton, Gives a Cotton Resource.
Corn, Wheat, Rice, Barley (is this still a resource?) etc... +1 Food on all Farms, Requires state access to denoted Grain resource, Gives an extra such resource.
Then you'd have unique ones:
Pepper Farm: +1 Gold on all Local Farms: Requires either already having access to Pepper, OR the same mix of local access resources as the building that we already have in the game currently that generates Pepper: Adds the Pepper resource.
And this list could go on. This is ONLY thinking in terms of Farms and only scratching the surface of what could be possible. Many of our current buildings already match up with improvements (You have a (Resource X) Mine available to build as a building in the city if Resource X is available in the city vicinity.) If we simply make a set of options and limit every city to only selecting one, we deepen our already amazing Manufactured Resource methods, and give a lot more strategy and a few less builds to pick overall.
As for being stuck with your choice as new options may emerge, a building can always be sold to pave the way for another and events could cause one to be swapped out for another if there's a far superior one available that the player may not have realized as it wasn't when they made their choice initially. (ex: Local Farmers have determined this soil is amazingly fertile ground for Peppers and in recognition of our need to increase our Pepper supply, they've begun to use Pepper Farms rather than Wheat Farms.)