I am saying that market based solutions are probably better than the alternatives. I think focusing on big corps/landlords is a completely wrong way to approach this issue as you're just missing the real problem of urban housing: it's a supply shortage and little else. Instead you're focusing on the symptom (increasing prices by landlords). Urbanization is progressing faster than construction can keep up with and that is the case practically everywhere in the world. Any shortage in market economies will drive prices up. If you have X people applying for a rental unit, you will have to make some determination as to who gets the flat. Your point is that making that decision based on return on investment is unethical (or I presume that's what you believe), I'm saying it's ethical because living in a city is not a necessity, even if it is (evidently) very desirable. Subsidies for refugees, low income workers and students notwithstanding, I support those. But clearly, all the non-social housing won't (and in my opinion shouldn't) be allocated randomly or by whatever else metric you're proposing. At the end of the day you must provide as much housing as possible to meet the demand and any policy that disincentivizes private investment and construction will harm the very group you seek to provide shelter for. If I cap the rent, investors will build somewhere else. We already know this. Just forget about landlords and think about how to maximize the amount of units built. Free markets aren't failing to provide sufficient urban housing because they're free markets - clearly, the market wants to provide as much as possible as there's unmet demand and therefore unrealized gains to be had. The question you should be asking is: where are those shortages and what do we do about them? Is it construction capacities? Bureaucracy? Zoning laws? Something else altogether? The idea that an entirely government run housing market could magically solve all the housing issues when a free market with a profit incentive can't, is quite honestly wishful thinking.
I grew up in the aftermath of a centrally run economy and I think short of dropping a nuke on my city, you couldn't have left it in a worse state. It took decades to recover. That said, a housing shortage was truthfully not among the issues we faced for a long time. It would be hard to believe anybody would want to move here given the state the city was in after the iron curtain fell.