Taxing land by value encourages efficient farming. It will make farmers want to economize on land, just like a carbon tax would make people want to have fewer emissions.

Also, the gini coefficient for landownership, by value, is actually higher than income virtually everywhere. Thus, a land value tax is actually more progressive than an income tax.

Taxing by market value also raises the most revenue, for the same reason why a rational landlord only wants to charge market rent. Charging either more or less is just leaving money on the table.

And if it is less, the difference will be pocketed by landlords. Because they know what the market value is.