A recent study on co-operative housing found that rents for equivalent-sized homes in equivalent neighbourhoods were 20% lower after 20 years in co-op housing and about a third lower after 30 years. I think the same would be true of any form of non-market housing simply because the rents are based on cost and not on profit.
Since the passing of the Dominion Housing Act in 1935, it's been recognized that low-income people's needs will not be adequately met by the private market and that we need 20% of housing to be non-market in order to meet the needs of low- and moderate-income people, particularly in cities.