from what i have seen, this is not the case because other places do not provide enough incentive to build new homes. vienna is growing faster than some other cities. it's not easy to find good numbers. maybe this helps: in 2021 in all of germany about 260000 new apartments were built. that's one apartment per 323 inhabitants. in vienna in 2015 11500 apartments received building approval. that is 1 apartment per 165 inhabitants. of these only one third were built with government support. while in the same year 100million euro of government support remain unused. but apparently, since 2020 it is not allowed to have more than 1/3rd of any new building project without government subsidies and rent control. unlike germany subsidies continue for the lifetime of the building and so they can't be used for speculation and thus ensure a steady supply of affordable housing.
because of viennas growth i suspected that vacancy rates should be low. what i found is that from 900000 apartments in 2015 35000 were empty. that's 3.8%. this is from a statistic made by the city. others claim estimates from 80000 or even 100000. in 2017 9000 out of 2009000 city owned apartments were empty (4.3%). most of those empty places are available on the market.
i could not find anything good on financing. apparently most of the money comes from rent-income, so it seems to be mostly self-financing, although critics claim that the city also does not spend enough on maintenance. the city can also save money because they already own the properties they build on.
so it looks to me like a successful non-profit operation.