How does infrastructure work with a land value tax?
Consider an area with 100 equal sized lots all with the same land value, and each with a one family home on it, with all the families about the same size. The area uses a property tax that is based on the value of the property including land and buildings.
That area needs roads, water, sewer, trash collection, electricity, schools, parks, and emergency services sufficient for 100 families. Each family pays approximately an equal share of that via their property taxes.
Now 10 of those lots have their single family houses replaced with 100 family apartment buildings. The area now has 1090 families instead of 100 families, and needs to greatly expand infrastructure.
Under the property tax the owners of the 10 lots with apartment buildings pay a much greater share of that expanded cost than do the owners of the lots with single family homes, which presumably gets reflected in the rents of those 1000 apartments.
It probably won't end up with each of the 1090 families in the area paying an equal share of the area's infrastructure. I expect the share for the apartment families will be less, but not massively less.
Compare to a land value tax. If the tax is just based on the land value won't each of the 100 lots pay the same amount? To pay for the need for 10x as much infrastructure the tax rate will have to up by a factor of 10. The result is that families in the single family homes will be paying per family about 100x as much for the same infrastructure services as those who live in the apartments.
And if some people build even bigger apartments, those tenants will be paying less for the same infrastructure than the people in the smaller apartments.
What is the justification for different families having to pay such different amounts for the same infrastructure just because some live in denser housing?