Did you keep in mind that for each settler you need additional culture when acquiring new social policies? It's probably not that clever to pump out so many cities that early.
+30% more per extra city. That's why I'd limit it to two.
Provided monuments were built first, you'd see a net gain in cultural spending for the course of the game and it'd probably be a wise investment to expand earlier than later since the incubation period required for a new city to reach it's fullest culture potential will grow as later cities are introduced with poor infrastructure and more culture buildings to build.
It'd do better as a long-term investment to expand earlier. When The monument is taken into consideration... Each city constructed will increase the cost of a policy by 30% yes... but once the monument is complete, you'll be gaining culture at a rate of 10% faster than before. You lose a bit of opportunity cost in getting your first few policies a handful of turns earlier, but I think the net gain will result in both faster and a great amount of social policies as the game progresses... Which naturally means a faster culture win if that's your goal.
Example to illustrate what I'm talking about;
1 city with a palace (manual says 1 culture) and monument (2) = 3 CPT, The manual states the first policy is 25... which you'll probably get before your second city no matter what... So let's just use a random number for example, let's say the next one is 50. It'll then take you about 17 turns to get to that policy. When you construct a city, it'll take about 22 turns... so you lose 5 turns... but that total is then modified again once you build a monument in the city and it goes to 13 turns... Which meant... if you could snap your fingers and plop a monument down there the net gain is greater.
Obviously, we can't do this... The reason why expansion becomes favorable is because when
temples come, we can do this. If we expand appropriately to out limits with disregard to the costs of policies rising (which fall back into balance after the monuments are built anyway...), when temples come online, we can proceed to construct them in as many cities as we see fit at the same time, resulting in no incubation period.
Further, when considering that 1 city with a mine can construct a monument in 20 turns... You figure in less than that amount of time, the city will recoup the culture "lost" due to the increased cost... granted no culture is actually "lost", so much as the opportunity to get a policy a few turns sooner. I think it may be more efficient to establish the core of your cultural empire quicker rather than later... cause once the cities are established and their monuments setup... the net gain will cause you to gain policies
quicker than if you had remained small. After that point you can increase each city's culture accordingly as you develop new technology.
The period of net cultural loss due to increased costs is made longer for new cities when you discover more and more cultural buildings because it takes longer for a city to reach it's full potential.
So in sum, if ever I were able to expand; I would as soon as possible.