By keeping people out, this will actually increase the scarcity and drive up "prices" even more. Your "big sum of money" acknowledges as much.
So this is a terrible, unfair idea. And if we were to ever implement such a scheme, the only way to make it remotely fair would to heavily heavily tax this wealth, perhaps by charging existing residents a highly monthly rent to stay, and for those that get a grandfathered-in prize, they should have to pay a large amount of capital gains.