This isn't even remotely true in the typical case. It is a lottery, to be a certain, but most NYC public housing is not in rich neighborhoods.
Living on the ass end of Bushwick, East Harlem, Crown Heights, and Coney Island is not opulent, nor has it ever been. All of these neighborhoods are still poor, and while some are gentrifying none of them can be identified in any way as upper class, or even upper-middle class.
There are notable exceptions - the projects on the Lower East Side for example were built when the neighborhood was one of the poorest in Manhattan, but in the past ten years has transformed into a playground for the wealthy with shiny new glass skyscrapers going up every which way.
The public housing system in NYC was neither intended as, nor does it generally have the effect of, mixing the poor with the rich. All of the complexes were built on what was at the time land that nobody ever expected would be worth much, the mixing of economic strata was not a major concern - in fact the design of the public housing system was in large part driven by a desire to segregate the poor.
Maybe 10 years ago, but the Jefferson L stop is mega upper class nice at this point. Indoor climbing gyms next to circus themed bars next to coffee shops with zen gardens, all within quick walks to public housing. Hell, I don't make enough money to get a lease off the Franklin Av stop in Crown Heights, at this point...
We already went through this a century ago during the last Industrial Revolution. Jacob Riis photographed all the many people living in the tenements. Society decided this was a terrible thing and that we wanted to at least provide a basic standard of living in America's richest cities. Hence public housing came into being.
Unfortunately it was never properly funded. It used cut-rate materials to do a literal poor man's version of Modernist architecture. Exclusionary zoning meant it could never really be co-located with middle-class or even wealthier areas, so the children of these families never got access to the same quality of public services or schools. When the demographic composition of public housing shifted from poor white families to poor black families, public support for it was just decimated.
It's not really "low-wage" if their rents are being subsidized, randomly.
I'd like to see a system where a council house is on a fixed term, say 5 years or 10 years, then it goes to the next person on the waiting list, and you can rejoin the queue at the back if you so desire. That's more than enough time for anyone to make a smooth transition to the rental or homeowner sector.
I believe many new tenancies are "starter" tenancy agreements; a probation period of 12-18 months. There are also fixed-term assured shorthold tenancies.
Tenancies started before 1989 are somewhat controlled by a council Rent Officer. Applications must be made to increase rent. Tenancies after 1989 experience yearly rent increases, capped to CPI I think.
There are also 'affordable rents', basically a way for housing associations to charge more for rent.
Not disagreeing with you, but social housing is quite different to the pre-1989 era.
(Actually, I think they have the option of paying the "contract rent", which is an approximation of the market rate, if that is cheaper for them.)
While this may be true, this is definitely not the only way to talk about public housing in New York (i.e. the whole city, not just Chelsea and other hot areas in Manhattan).
Unless you are going to legally stop people from moving out, you are going to figure out how much you can keep the factor you apparently need -- rich people -- while letting as many poor people as possible benefit from being in a mixed-income neighborhood.
Even if you aren't a bleeding heart, even if you accept greed as positive virtue, you can't expect to live completely separate from the poor, esp the working poor who actually do jobs in the actual city, and many of whom probably start work earlier than you wake up. Do you really want your trash collector to commute in?
Yes. I think it's important to have disparate classes living together in a dense urban environment, rather than a homogeneity of wealth.
In fact, I believe that attention to this priority is one of the main reasons that NYC is the greatest city in the history of world civilization, versus the bland expanse of stripmalls, chain retail, and cultural drought that defines the American living experience in many other areas.
Well then, go on, argue. :-p
There has been quite a few cities in the last few thousand years...