When did public housing get so luxurious?

Question: Is it an effective use of space for PHA to build green, single family public housing with public funds?

As someone who works hard to afford my first single family home, which I bought just three years ago after renting apartments over my whole adult life - it bothers me to think that my tax dollars are going for single family homes with island kitchens and lawns when there are many more needy people who'd be happy (and warm) living in apartments that could have been built on the same space.

The idea with low-income housing is to give poor people a home while they work to improve their circumstances to the point where they can buy or rent a home of their own, that they can choose and modify to fit their needs and tastes - to participate in the American dream of home ownership.  Therefore, what does it say of a Public Housing Authority who builds homes that exceed the expectations of many non-section eight first-time home buyers?  If the public housing is better than what can be afforded otherwise, why would anyone leave public housing to open it up for the next needy family? 

Coming from New York, home of the high-rise housing project; I've seen many crime and public health problems involving public housing, but one has to recognize that a cluster of 10 to 20-floor apartment buildings puts a roof over far more heads than a cluster of 3-bedroom single family homes.  Isn't that the objective of public housing?

One has to wonder why our Public Housing Authority fails to see why that objective is so important when building properties with OUR MONEY.