Because birth rates are going down worldwide and at some point the people who wanted to move away from the countryside/poor countries to the big global cities w

Because birth rates are going down worldwide and at some point the people who wanted to move away from the countryside/poor countries to the big global cities would have already moved (those left behind are older than the ones leaving, so such places will have even lower birth rates). The major global cities will still grow in the next 200 years compared to now, just not as much as they have the previous 200 years.