>large parts of countries like India, USA, China, etc are unpopulated. This would imply that a one-child policy won't help, or really any population control me

>large parts of countries like India, USA, China, etc are unpopulated. This would imply that a one-child policy won't help, or really any population control mechanism -- the problem is then is that wealth is too centralized in too few cities. If you cut the population in half, they'd still all end up in Delhi. The population chooses to be excessively dense (excessive in regards to their infrastructural support) -- they aren't being forced into it (because as you say, there's space available). So to solve it, you need to address why they go to the city in the first place (despite the danger)