I definitely like the goal of encouraging players to have 3-5 cities max by end game while still letting other settlements contribute.
I disagree here. I think there are some civs which are designed to be played "wide" even before the modern age.
For example, the unique quarter of the Majapahit gives +10% gold towards converting a town into a city. This is a weak bonus if a lower number of cities is considered to always be preferable.
I actually think that this unique quarter in particular demonstrates the issue I have with the +10% cost increase for each city. Because this cost increase actually penalizes you for making a lot of use of this unique quarter, which I think are supposed to be widely used.
Also consider Spain. The Siglo de Oro special ability also gives +15% gold towards converting towns into cities, even +30% in distand lands. Every time you invoke this ability however, the cost for buildings now increases for every city. So if I play Spain, should I not convert a lot of towns into cities in distand lands?
There are also a lot of traditions which give a bonus to cities only, for example "Throne of My Fathers" (Aksum), which gives bonus gold in coastal cities. So I think that Aksum is also designed to be played with a lot of (in this case coastal) cities rather than towns.
Therefore I think there should not be a universal goal of having 3-5 cities max by end game. The optimal number of cities should instead be based on specific playstyles for each leader and/or civ.
EDIT: Mongolia also has a civic which makes converting captured towns into cities cheaper.
In my opinion these effects (which give extra gold toward converting towns into cities) give you a larger benefit the sooner you convert a town, because the gold cost of conversion is less for larger towns. But this also means that you have to use this ability when the newly converted city will be the least productive, which makes the resulting cost increase for buildings in
all your cities very penalizing.