It is nothing. For public housing to make sense it has to be a considerable amount of the supply, and be universally available, not only for low-income people.
[1]> NYCHA has approximately 13,000 employees serving about 173,946 families and approximately 392,259 authorized residents. Based on the 2010 census, NYCHA's Public Housing represents 8.2% of the city's rental apartments and is home to 4.9% of the city's population. NYCHA residents and Section 8 voucher holders combined occupy 12.4% of the city's rental apartments.
1 out of 20 of the city's residents, 1 in 8 if you count voucher programs. That's far from nothing, but you're right, there's definitely room for improvement if you can cut through the red tape of nimbyism and corruption.
