Small city resident checking in here, 1br apartments are going for $1500/mo on average here, and we're considered an extremely affordable place to live. The average person I know carrying a mortgage has a payment below that for much more living space.

What I would say we're missing is condominiums in the city center. Lots of apartments, fewer places to own in the inventory of downtown housing.

But does it matter? The way housing problems were always fixed was very simple and without any kind of tax: with the government building social housing, allocated according to social principles (you pay the same, but the size of the apartment is determined by the number of kids you have). A LOT of non-luxury housing. This has nearly stopped. These buildings were famously bad. First, they tended to be unfair and violate building codes, they were government projects (ie. cost a lot more than a luxury housing development despite being much worse), and since houses got allocated by the government to vulnerable groups, they tended to have safety issues in the first few years they existed.

But they fixed housing. A decade or so after they were built and things became somewhat stable around them.

The problem with tax, and any kind of economic system is very simple. Capitalism and communism, and the more creative options like mercantilism or militarism, we can argue about them for a long time, but fundamentally they divide up existing properties. Nothing more. We can use these systems to choose WHO is homeless, but they cannot lower the number of homeless.

It encourages supply and liquidity in the market. Individuals will see an opportunity to undercut the large investors if they're hoarding property, so will build new property if they can't get their hands on existing properties. And if it is no longer feasible they're likely to sell rather than hoard for property appreciation.

If they could simply "pass that cost to their renters" why wouldn't they just raise rents to that level now, absent any tax increase?

The point of this progressively increasing tax would be to raise the landlord's costs to the point where the market actually cannot bear a rent increase--which would disincentivize using the property as an investment.

Yes, a nonprofit group running/developing a housing area and renting to its members is much nicer than having to own at least a condo and then dealing with a bunch of bank/lawyer/realtor nonsense every time you want to move.