I think the housing market plan doesn’t seem likely to work. The real issue is not that current landlords are exceptionally greedy (the rules of capitalism assume and encourage everyone to be as greedy as possible), it’s that there isn’t enough housing stock to give everyone who wants one a unit. In economics, housing is more or less a commodity like everything else and thus follows the usual rule of supply and demand, i.e. insufficient supply drives up price until demand tapers down to meet it. If you buy up the city’s housing supply and then price them below the equilibrium price, the result will just be that far more people want a place than you will ever have supply for, since you are not actually creating any new housing supply, just buying existing supply from other people.

I would think you’d have more success getting into the property development and construction business, buying up vacant or derelict lots in the city, building them into blocks of flats, and then letting them out on the cheap. You’d also have to hire lobbyists to prod the council to change zoning laws to allow for this development and obtain planning permission. It takes a lot of political maneuvering to make a housing project successful, not only because of legal restrictions, but also because you’ll need amenities for your new development. Parking is a big one in the US unless you build a dense mixed-use development which is bureaucratically difficult to get planning permission for, but there’s also considerations like whether the nearby bus line can handle the influx of passengers, whether the neighbourhood school can handle a hundred more pupils, whether there’s a grocery store nearby, whether the area “feels safe”, and so on.

Kind of the reason why State-run public housing schemes are so successful is because they are a government agency that has the power to brute-force the solutions to these problems. Zoning codes? Overruled. Public transit? Ordered. Schools? Built. Private developers don’t have the power to do these things and have to beg the council for them instead.