The only thing I have for comparison is Imperial Rome, which grew beyond a million in its heyday. However, Rome was at this time a city where most of the citizens were either completely or partially sustained with state- and privately funded handouts of grain and gold, in exchange for political support, not to mention a large net immigration.
So, if I understand correctly, the main reason for Rome to grow that big was that the emperor and the political elite needed loyal citizens (clients), and used their extensive economic network to pump in resources produced by slaves in different parts of the empire to sustain the city. Cities of this size would otherwise not be possible with pre-industrial means, and most other Roman cities were of sizes more comparable to Medieval European cities.
So how, and why, did Kaifeng and Hangzhou grow so enormous? Edit: In the case of Kaifeng and Hanzhou, I'm speaking about the Song dynasty specifically, but any pre-industrial Chinese 1 million+ city would be very nice to learn more about.
Side question: Is it widely accepted that they did in fact grow this large? Were they truly one city or more of a region?
At least for Lin'an (as Hangzhou was then known), the population increase (for the city and the region as a whole) was not a planned thing. For a good period of time leading up to and following the relocation of the Song court to Lin'an, there had been a steady influx of Northern migrants who were fleeing the multi-party wars in the North.
This had a major impact on the languages of the region as well, which is my particular focus on this time period. The Yangtze Delta has always been a focus of immigration well before the 20th century.
It wasn't that someone said "lets make this place huge" so much as it was already fairly well populated, and then wars in the north pushed a huge number of people into the area. Why the Delta and not somewhere else is because the area was already fairly well off and had the ability to support the numbers.
In case you have follow up questions I'm actually in the field at the moment so cant get online so easily. It might take a while for me to respond, but ill definitely try.
However, Rome was at this time a city where most of the citizens were either completely or partially sustained with state- and privately funded handouts of grain and gold, in exchange for political support, not to mention a large net immigration.
This isn't really true. The grain dole in Rome only applied to perhaps a fifth of the population (it varied historically, but Augustus limited it to about 200,000), and this fifth was by no means the poorest. Furthermore, the grain dole is not an "active" policy, rather it was a reaction to the expanding size of the city, which some Republican politicians responded to by offering free or subsidized grain. Rome had no policy aimed at increasing the size of the city even if that was often the effect.
That being said, the Roman government did take action to secure the grain supply, ad in this respect it was quite a similar situation in China. To go somewhat against what /u/keyilan said, while Chinese imperial administration never explicitly encouraged immigration, it expended incredible amounts of energy making sure the city was fed, up to and including the famous Grand Canal. So while they may not have intended the city to grow, the side result of their policies was that the city was an attractive destination for migrants.