Any tax is "arbitrary" in the sense that there's no natural law dictating what should or should not be taxed, it is up to our best judgement. Carbon taxes and garbage taxes make sense, thus why I stated in my comment that LVT is logical as a
primary tax, not the
only tax.
Currently most federal tax revenue comes from wage/payroll taxes (65%). There is nothing less arbitrary about taxing wages than land value. In fact, taxing wages is more harmful as I will explain.
In general the more you tax something, the less of it you get. So by increasing income taxes, we discourage working - something that is presumably beneficial to society, while also encouraging more people to evade the law to avoid the taxes (working under the table). Land value however doesn't have any of these distortions because land supply is fixed and nobody creates it. Unlike income or sales taxes, land value tax is impossible to evade.
The reason to tax land value is because nobody is more entitled to the land and commons than anyone else, land value gains are pure unearned income, and taxing land has no negative distortions. By not taxing land value, we give a free ride to the landowning rentier class, and encourage the zero sum economic waste of playing land speculation, leading to housing booms/busts like the 2008 Great Recession and 1986-91 Japan housing bubble.
> Why should a low-margin supermarket which people need, occupying tons of space, pay huge taxes, while a tiny very profitable ultra-luxury boutique hotel pays only 5% of the taxes?
Land value is largely determined by location. That supermarket may have a lower tax bill than that boutique hotel in the city center if the supermarket is located in an area with lower land values. LVT promotes denser and more efficient development, and thus a supermarket could be located in the basement of a residential apartment complex or mall and pay less in land value taxes by sharing the tax burden with the rest of the land property.