You can in Manhattan. The tallest residential structure in the U.S. is going up within a few blocks of Central Park.
http://nymag.com/news/features/foreigners-hiding-money-new-y...
If a bunch of billionaires want to pay property taxes while using barely any city services that sounds like a win to me. We can use that money to provide better services to the people that do live in the city year round.
In my observation the people who are most bitter about billionaires "buying up Manhattan" are the multimillionaires who want to be on the top of the heap.