The fact that those cities are so expensive is exactly the problem. Those cities are healthier if they have a healthy mix of different population groups. I live in Amsterdam and would hate to see it become a rich people's ghetto, though it's definitely at risk of that happening. Maybe it already is.
Where are the people who work in those cities supposed to live? Are they expected to commute an hour a day, diminishing their earning potential and increasing their expenses? People in the wealthiest cities also tend to have access to more resources, due to the concentration and diversity of the population. Denying low and middle income families access also diminishes their potential, while diminishing the potential of cities through the reduction of diversity.
At best, this sounds an argument to hold people back. At worse, it sound like an argument to push people down.