In the U.S. and in most developed countries, we've had (1), in some cases (3) but (2) is become scarce.
In my opinion, there are very few modern cities that are able to provide cheap housing these days. It requires an activist government fighting two very powerful forces: existing home owners and corporate landlords. Truth is that the lobby of those interest groups are way more powerful than low income renters.
The other problem is that expanding the housing stock is not sufficient, governments have to provide basic services: water, public transportation access, sewage, etc.
Who is going to pay for them? In most cases, the cost is paid via property taxes (existing homeowners and corporate landlords)
The truth is that we have disincentivized the creation of new housing stock and until we fix the underlying issues of bringing more supply to the market, this issue will continue to worsen.
https://www.zillow.com/research/new-construction-shortgage-2...