When free-market housing have to compete with non-market housing (public or associative) in multiple segments (not only social housing), it works really well as a free market. For that, you need between 20 and 40% of the available housing to be non-market though.
That seems like a general thing, not specific to housing. Having the government provide some kind of basic service in all essential areas would do wonders to provide a baseline for the market. Private businesses usually complain about "unfair competition", but if you can't provide the service that is either better or cheaper than government does, why should we care about your business at all?
Singapore, especially, has very intentionally set many laws and regulations, specifically to promote the idea that their people have a place to live, with the vast majority of people living in government provided housing.
> with the vast majority of people living in government provided housing.
Citizens you mean. If you are an expat or migrant worker, your choices are a lot different. 3.64 million citizens in Singapore vs a population of 6 million.
