> All taxes except the land tax cause some sort of dead weight loss, which just leads to lower spending and economic activity, which leads to more unemployment.

Land tax does the same thing. If you try to generate all tax revenue from land tax then land tax is really high. Land tax is set based on the value of the land, so land in the city center becomes even more expensive than it is already and you increase the incentive for sprawl by not allowing the owners of the best land to recoup its value themselves, which deters investment there. (Property tax does this too, and moreso, because it taxes the investment in buildings as well; but trying to get 100% of tax revenue from property tax would be problematic too. It's bad enough as it is.)

> Most valuable land is owned by the wealthy, and most poor people rent, so I don't see how a land tax would fall on the poor more than the wealthy.

Rents are always proportional to ownership costs. If it cost much less to rent than own then the existing owners would sell their properties to by non-real estate investments until property values fell to parity. If it cost much more to rent than own then investors would bid up property values or build more properties in order to get those returns, until that wasn't the case anymore.

If you increase the cost of property ownership, you increase rents, and vice versa.

> A land tax cannot be passed onto a tenant, since the supply of land is fixed, and so taxing land doesn't changing the supply-demand curve (leaving the equilibrium price the same).

Tenants don't buy land, they by housing units. You can build more housing units or not on the same land.

> the tax will always be paid (either they keep it, and pay the tax, or sell it to someone else, who can then use it).

This is the basic flaw in the land tax theory -- that somebody has to pay the tax.

A piece of undeveloped land in the city center starts off as very valuable, so it has a very high land tax. Anybody who wants to buy it had better be getting a very large return. It makes it more profitable to buy one plot of land and build a 100 story building on it than to buy ten plots and build 10 story buildings. So enough people do that and break even from that to saturate the local demand for real estate.

But then there are those other 9 plots which are now empty, or still have 5 story buildings on them, next to the 100 story buildings. There isn't enough local demand to justify any more 100 story buildings, but they're paying the same land tax as the 100 story building next to them because the land is of the same type and in the same approximate location, so they're completely bankrupt. The land is worthless because the tax is more than the returns you can get from it -- you can't build another 100 story building because the rental market is saturated and its existence would lower rents to below your cost, but nothing else brings in enough revenue to pay the land tax either.

So you abandon the property, or donate it to a non-profit which doesn't pay the tax, and the tax is thereby avoided.

So in the most desirable locations you end up with a handful of very tall buildings next to a larger number of abandoned lots. That is not efficient land allocation.

Meanwhile in the suburbs the land value is not very high because it isn't as scarce (compare how much land is in the city center to how much is in the suburbs around it), and affluent people like to live there anyway, so everybody with money is living there and paying low taxes. And even there you might get the same thing -- a few 20 story buildings that completely fill a plot of land where people live, surrounded by empty lots.