The reason economists say that a tax on land value is the "least bad" tax is that such taxes have no deadweight loss. Any tax on production or exchanges or movable assets causes economic inefficiency. A tax on these things causes a deadweight loss (i.e. allocative inefficiency) because people who would have more marginal benefit than marginal cost are not buying the good or service — just as a subsidy induces people to buy who impose more marginal cost than their marginal benefit. However, this effect of taxation does not happen when the supply of the taxed good is perfectly inelastic, as is the supply of land — more precisely, the surface area of the Earth. Sites cannot flee or evade taxation, and the available amount of them is not reduced when they are taxed. (When a tax is not on a good but rather on a "bad", like pollution or congestion, it's the very absence of the tax that causes allocative inefficiency, because external costs are not internalized.)
Taxing land value is not only more efficient than taxing production or exchanges, but it is also less intrusive. All the government needs to know is who owns each plot of land and how much the unimproved land is worth. Appraisers and insurers make such calculations routinely, and one variant would have each land-holder self-assess as long as he's willing to take any offer over his assessed value. There's no need to audit anyone's behavior, as with taxes on income/production/exchanges. You don't even need to visit the site or look over the fence, as you do with taxes on land improvements or square footage. For illiquid landholders, taxes could accumulate as a lien against the property, capped at its market value, so nobody need ever be taxed off the land they hold.
Land value taxes need not even be strictly mandatory. If you as a landholder decline to return to our community the ground rent you appropriate from us, then we could simply disconnect you from our wires and pipes, and while you’re in arrears we could publish your name, address, and photo as someone whose property and person are excluded from the protections of our LVT-financed police and courts. If we catch you using any of our streets, parks, or other LVT-financed public goods, then you would owe the arrears on your parcel's land value tax, per the terms of the no-trespassing signs prominently marking those public goods.
Land value taxes are naturally local, and so encourage Tiebout Sorting. If the the local mix of government services is too high (or too low) for your taste, or if they aren't a good value for the LVT rate financing them, then you can vote with your feet. By contrast, income and sales taxes tend to get centralized at the state or even national level, because (unlike land) income and sales can flee to lower-tax jurisdictions. (New Hampshire is among the most free states, and gets the highest percentage of government revenue from property taxes. California finances its high government spending with high centralized state income taxes that rose after Prop 13 restricted local property taxes in 1978.)
LVT retrieves the extra land value created by public services — streets, pipes, levees, police, parks. This creates pressure to defund public services that do not actually add value in the free market for land.
LVT turns out to closely model how consensual private communities tend to govern themselves. Malls, business parks, hotels, condominiums, homeowners associations — all tend to "tax" their tenants not according to profits or revenues or inventory or improvements, but mostly by site value (for which square footage is often a good proxy).
LVT imposes a built-in ceiling on government revenue. Critics of land value taxation claim it wouldn't raise enough revenue because ground rent is allegedly only a small fraction of GDP. That sounds like a good thing to me. If government revenue is restricted by definition to ground rent and fees for polluting/congesting/depleting the commons, then government cannot be nearly as big as when it is allowed to tax labor, production, exchanges, and all resulting products. Once you have taxation of people's labor and exchanges and produced assets, there is no limit to what the government can take from you.