Live somewhere for at least 35% of a year (more than 1/3rd), then most of that tax goes away since it's a 'primary residence'. (35% to allow for moving as well as possible 'sunbird' / 'winter/summer homes', while still catching anyone who treats housing as an 'investment' (a tax upon the poor))

So the end result, the poor pay more?

Instead, what Vancouver did was simply tax empty housing.

Why is that framing preferred over "landlords, who reduce housing supply by keeping properties off the market"?

If you want to get to the root of the problem, look at the development process. Start with your local zoning laws. It is insane how tightly prescriptive they are, usually, and they generally have lots of density-limiting provisions like mandatory parking, maximum floor to area ratios, maximum heights, minimum setbacks, etc.

And then there's the planning/approval process.

They don't reduce housing supply for living, but they do reduce housing supply for owning. Normal people being able to own the house that they live in seems like a reasonable societal goal to me, but the current economic climate is making that harder and harder as houses move into the hands of landlords (private and commercial).

Yes, the world needs some amount of rented housing, but a huge percentage of people renting now want to own, just to have stability and control over their living environment.