I mean the law wouldn't just be "landlording is illegal" you have stuff in there to prevent these leeches from keeping them empty out of spite.
I would say that owning 3 homes for personal use is just fine and anymore than that is illegal. Also not hard to look at a landlord and see what properties they are renting out and what properties they live in and force them to sell the properties they use to rent out.
I don’t think you’ll see the results you want out of this. Instead what you’ll see is that the rental companies will shut down and divide up their properties among their shareholders so that each shareholder ends up with 3 houses (or whatever number you set as the limit). If there are too many houses and not enough shareholders then they will sell more shares until the numbers work out.
Not billions, but thousands to millions. Many, many investments are owned by pension funds and the like. You know, regular people’s retirement funds.
You keep wanting there to be a villain in this story but it’s just not the case. Sometimes societal problems are caused by collective action with misaligned incentives.