Owning buildings, yes. In this hypothetical and ridiculous scenario, the only people buying would be those who intended to live there. This would decrease prices (it is no longer a speculative asset) and increase home ownership rate. Functionally no one would own a whole apartment building just to rent it out. Individual units would end up being sold the way condos are. Building "apartment" buildings would still be attractive, because they could be sold as condo units. With no one willing to rent, there would a more direct demand from actual buyers.
Let me once again reiterate that the 1M/day vacancy tax is an obviously ridiculous proposal, and any real-world policy would have many more caveats and be orders of magnitude less radical. But even something so obscenely and grossly unrealistic has potential for solving the supply issue, so we should be considering the more moderate solutions.
Even then no, I build a 30 unit building, covid 22 hits, nobodies buying, I'm on the hook for 30mm / day. Nobody would even build with that risk. You'd have low density housing, single unit homes and massive traffic/pollution issues often associated with suburban sprawl.
Yes, 1m/day is hyperbolic, but if you put the constraint on the suppliers (builders, owners), and the demand is inelastic (you've got to live somewhere), then the outcome is to constrain supply for maximal benefit.
2) A builder can hypothetically continue "building"/renovating the units indefinitely until they have a buyer. Alternatively, nothing about this hypothetical scenario requires the original constructor to even pay the $1M in the first place - it could be deferred, or be another rate entirely.
Side note) Landlords/owners aren't suppliers, they are speculators.
Let me once again reiterate that the 1M/day vacancy tax is an obviously ridiculous proposal, and any real-world policy would have many more caveats and be orders of magnitude less radical. But even something so obscenely and grossly unrealistic has potential for solving the supply issue, so we should be considering the more moderate solutions.