Since this incentivizes increasing the housing supply, zoning would quickly change from exclusionary to abundant. With those new homes being built, people would choose to move from their worn-down house into something new and better, and their current property would eventually have the same fate. It's not kicking people who love their homes out, it's letting people leave their homes for better ones.
You would still have apartments. You would still have AirBNB's. You would still have co-ops. You would still have houses.
Any tax money in excess of what is currently paid would be currently would simply be given back as a citizen's dividend, unless that tax money could be better spent on infrastructure, infrastructure that would pay for itself in higher land taxes that would yield even more land tax share dividends.
When you tax land value, the initial price of the property drops to offset, which makes it easier for less wealthy people to afford a down payment. A perfect land value tax would set the price of land at zero with a hefty month tax payment.
If this raises more tax money then the government can meaningfully spend, you simply give it back evenly to the community. Note that, just like the carbon fee and dividend system, still incentivizes that people use as little land as they can.
[0]: https://www.strongtowns.org/journal/2019/3/6/non-glamorous-g...