How would it encourage urban sprawling?
Obviously in real life, people care about other things besides just pure acreage, but you can see the argument.
As I explained in another comment[1], a property tax discourages density and encourages sprawl. A land value tax, on the other hand, does not have these adverse effects on density because it taxes only the fixed supply of land, not the variable supply of buildings.
It would certainly discourage the building of houses in the city centre.
No, that's not how it works. The value of a property is made up of the value of the land and the value of the buildings on it. If one of these two components is taxed, its value is reduced. However, it is important to remember that the supply of land is fixed, but the supply of buildings is not. If one taxes buildings, as is the case with a traditional property tax, construction activity is reduced, but if one taxes only land, as is the case with a land value tax, construction activity is not impeded at all. That's the beauty of a land value tax: it doesn't distort anything.
With a property tax, an undeveloped lot in the center of town is taxed less than a high-rise. With a land value tax, both are taxed at the same rate. Relatively speaking, a property tax promotes sprawl, a land value tax promotes density.
Who would want that house with that tax bill?