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 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.
[1] https://en.wikipedia.org/wiki/New_York_City_Housing_Authorit...