I am not a proponent for taxes, most of my arguments centre around the idiocy of most taxes. And you are correct in your analysis, particularly as the improvement component on the land is already taxed by sales taxes for the materials and income taxes for the labour.

However, it's best to tax broadly and close to the generation of income.

I think land taxes couples with sales and income taxes is an efficient combination. Land taxes penalise land banking, and encourage the most efficient use of land.

Sales taxes penalise consumption, and encourage savings or investment.

Of all, income taxes penalise earnings, but earnings are unavoidable for most people. But they do incentivise investment income where there is a differential, which could be mildly beneficial.

The key to all these is uniform applicability and flat rates. The massive drag that tax minimisation has on an economy is underestimated routinely.

From the property front - land taxes should be paid annually, there should be more releases of land with fewer restrictions, and there should be no/minimal transaction taxes to go in/out of a property.