Collinson, Ellen, and Ludwig have a new and long NBER paper (pdf) devoted to that topic. Here are a few bits:

The United States government devotes about $40 billion each year to means-tested housing programs, plus another $6 billion or so in tax expenditures on the Low Income Housing Tax Credit (LIHTC).

Yet total subsidies for home ownership may run as high as $600 billion, most of those not going to the poor.

There are over twenty different federal subsidized housing programs and most of them are no longer producing new units.

I am speaking for myself here, and not for the authors, but I cannot imagine any better case for cash transfers than to read this 75 pp. paper.

How about this?:

In 2012, housing authorities nationwide reported more than 6.5 million households on their waitlists for housing voucher or public housing.

That to my eye suggests targeting this aid is not working very well.

I found this to be an interesting comparison (I am not suggesting it is being driven by these federal housing policies):

The median renter household in 1960 was paying approximately 18 percent of his/her total family income in rent; the equivalent figure today is 29 percent.

Overall, I would like to see more economists call for the abolition of these programs and indeed some approximation of laissez-faire toward housing more generally.