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Many economists do support the land tax, but think it is too low to support government functions. I think a better criteria is - restrict the government only to the extent that you can support with a land tax, since a land tax is basically the approrpriation of a positive externality(civilization all around you)
Why can't the rate just be set higher?
When the tax approaches the rent of the property, the capitalised land value drops to zero. If the land tax is based on percentages, you'll have the rate escalating way beyond 100%. No problem for homo economicus, but most real world people would be shocked by seeing property tax rates of 100000%.