In my mind, LVT only works properly when you've ripped out every other tax: income, sales, capital, you name it. Absolutely no more friction and warped incentives. Divide the government budget by the weighted land values and tax accordingly. But that could never work in our world. There would be too much temptation to add a small tax here for this other thing, and then it snowballs, and then we're back to where we started but this time LVT plus numerous other taxes.
Of course, we should first replace the existing bad taxes for multiple reasons. Nonetheless, as a matter of economic and social justice, -any- amount of land rent that exists should be publicly collected and distributed on a per-capita basis.
This does not increase the user-cost of land as land has no cost of production. Of course as a transitional issue there will be net winners and net losers (for which we could create policies to address the transitional effects). The ultimate effect of the full public collection of land rent would be to bring the selling price of land down to $0, while the rental value would remain the same (not counting the dynamic effects).
In reality, land value taxation isn't really a tax when properly understood. You either pay a previous owner in selling price or you pay the public the annual rental value. Most people don't properly consider that the selling price is simply the capitalized ability to capture future rents. In an ethical society, this privilege would not exist.
For consistency you also have to tax accumulated past labour and intellectual property.
I'm very fond of self-declared valuations with enforced sale back to the commons if anyone is willing to front the value.
Add a tax free threshold a bit above the mean wealth so anyone can declare their 100k house is worth $1m or whatever without risking paying the costs of moving due to someone maliciously forcing sale.