Yes, but as i said, thats not part of the cost of the CD. Its a seperate investment, a very good one too.
Since you usually can choose between tiles producing more food or production, i value food and pruduction as the same in all calculations. I value gold 1/3 production. For now i value science / culture about equal to production because i dont yet know what else to do and it feels more or less correct.
Hence, according to my calcustimations repay times look more or less like this:
Settler: 20 + 3n turns.
Citizens: 5 - 8 - 11 - 15 - 18 - 22 - 26 - 30 (assuming you have tiles with 4 total production/food to work)
Early worker: 17 + 1n
CD with free envoys*: 20
CD without evoys: ~120
Trader: 10
CD without envoys but combined with trader: 25
CD with free envoys and combined with trader: 14
In civ i take 20 turn repay time / 5% ROI as a benchmark average.
Growing a city up to size 7 (actually used the formula now) falls roughly within this, after that it starts becoming what i consider a poor investment. That is of course assuming you have housing and amenities available for "free". pretty much meaning you have built farms or camps, which in turn only makes sense if you use those because you want to use other high production tiles with <2 food. If you have to add the ~20 production from granary cost (20 per housing + 20 for the 1 food), then your repay time is about 6-7 turns more for your citizens and thus, the 5th is the last decent investment. Well, we all knew by experience that it is about that size that we feel growing our cities becomes too much of a hastle, but i like to see it in numbers.
For some citizens might not seem like an investment but something that happens automatically, but for me it is a rough indication of where i prefer production tiles over food tiles. Of course other factors go into that decision as well, but it is clear that for a tiny city, i will prefer food while for a bigger one, i will prefer production as long as i have any decent investments to make. For a size 1 or 2 city, the value of growth is so big that choosing 1 food over 2 production is not insane. For a size 7 city i will pretty much always prefer production over food. Size 3-6 is where it depends on available tiles (If there are no more 4yield tiles available, the value of the next citizen is much less), available things to build and the wish to get 3 districts or not.
The early worker is a decent investment. Later workers might be a little more expensive, but they will have 5 actions and the tile improvements might be worth 2 production/food. That will make them totally awesome investments, potentially with repay times below 10 turns. (not even counting the forest cuts that allow the worker to pay for itself right after production)
Only the first settler seems a decent investment, the civic that makes them cheaper allows for a few more settlers to be a decent investment just by themselves. Of course the fact that the extra city allows you to make other awesome investments (citizens up to 7, tile improvements, commercial districts) makes that you can build lots of them before they really become bad.
Commercial districts by themselves are terrible. With either a trade OR an the effect envoy effect of CSes, it becomes decent. Only with both, it becomes really very good.
When do you build a CS and when not ? First of all, you build one when you have no better investment to make. When you have better investments to make, you do those first. So that may very well depend on when you expect to have the envoys and CS bonusses going. When you have those, the CD is one of the best possible investments. Workers right after getting feudalism are probably an even better one though and therefore can have priority. As long as you do not have the CS bonusses (and also probably your trade routes might not yet be worth 4 food/prod), you may want to prioritize settlers, workers, or units. (cant really calc the repay time of units, but we all know they are an awesome investment in civ6)
Again, im sure much of this is what most players were already doing. I am aware that all this number stuff may seem useless
Beyond that, you stop making them when it is so late in the game that it is better to focus on your victory condition. If the repay time is 14 turns, that is NOT 15 turns before the end of the game but quite a lot earlier. Cant really put calculations on this though, choosing the right moment to swich from growth to victory condition is the key to early victory dates. If you can read GOTM8 threads you can see i made the wrong choise there
*You do get the envoys for free, but still they do have a price of course as using the first ones for commercial district boosting means you are not (yet) enhancing your science districts or industrial ones.