Property taxes are calculated on the value of the land and the value of the structures. So current land value taxes would be about $2000. If a state were to pass a land value tax, it would calibrate it so that it offsets a reduction in the tax on structures. The granny would probably pay $5000 in land tax and $5000 in improvements tax. Only in an extreme case would she pay something very different, like maybe she lives right next door to a train station. In which case, she could probably sell her property for $10mm. I’m sure policies could be designed such that she would not be forced out until she died and then some of that $10mm gain would be collected in back taxes.
But that's not how a land tax would work. The idea is that it captures most of the value of the land (removing the rent seeking ability). So the tax would be at a level that makes owning the land itself not very profitable, it's the improvement upon the land that offering return on investment.
So you'd likely see a $1M plot of land taxed at $100,000+ per year. It would make zero sense to sit on the empty plot or build a single family home. It would incentive someone to building a $10M building on it.
