This is the particularly American way of implementing public housing, which, if I recall from my reading on the subject, is largely agreed upon to be terrible.
It is absolutely toxic to government programs to conceive of them as, essentially, 'poor services for poor people', the way American governments have so often implemented them. Specifically with public housing, you want this to be accepted by as wide a range of your urban population as practically feasible, so the government shouldn't restrict affordable housing arrangements to only poor people, but rather include people from all walks of life.
As an example how to get rid of the "public housing" stigma that seems so prevalent in the US, in Munich, the municipal government provides partial financing to apartment complexes that house a certain proportion of poor people, so a number of brand new apartments is open to people from disadvantaged backgrounds, while the rest would still be availabe on the free housing market.
A different take is what the city of Vienna did in the 1920s and then again in the 1970s, which was to engage in a massive public construction program, and then hand out houses based on relatively relaxed income restrictions that would still allow people with middle class backgrounds to get an apartment with massively reduced rent compared to the private housing market.
In either cases, these programs resulted in areas that largely avoided ghettoization and stigmatization, either by blurring the line of "public" and "private" housing, or by simply making public housing so common that it didn't acquire a stigma to begin with.