You can't deduct depreciation on an owner-occupied house to begin with. The premise is that you're trying to distinguish between landlords and people who have a second home for themselves. But they can just rent it to a friend who in turn lets them use it.
If they're buying multiple homes to rent out at market rates to the general public then they're just an ordinary landlord -- the thing that wouldn't be paying a tax on "second homes" by design.
I thought the tax on "second homes" was a tax on landlording and speculation, not a tax on vacation homes. I think we might just be talking past each other here.
Why would taxing landlords reduce housing costs? It just increases housing costs for landlords, and in turn renters, as landlords become unwilling to pay for new construction until rents increase to cover the tax.
If landlords become unwilling to pay for new construction, that reduces the demand for new housing supply hitting the market. Which reduces its price and makes it more affordable to owner-occupants.
I don't know if it definitely works. But it's plausible. Tax what you want less of, right?
