Well, economists often suggest a better way than just let the rich take over: directly subsidize people, not flats. So, if you want a neighborhood to not just attract bankers but also families with kids, pay the families for living there! The idea is to pay them only while they live there - independently of which accommodation they choose - and stop the payments when they move away. This way, the market isn't distorted, people don't get "sticky" in their ability to move to other apartments, and the whole setup is much more fair, as it's pretty easy to control who gets which benefits.

The downside, of course, is that the cost of such payments is far more transparent to the public. Many economists would argue that it's in fact much cheaper, as you it's more efficient. Still, today's subsidies are well hidden and almost never show up in household budgets. And thus it's hard to get to a system of direct payment.