That still leaves the question of what you want to do. Moreover, that doesn't mean that all of the distortions are equal. Land value tax has fewer distortions than property tax[1], and property tax is differently distorting than various other taxes.

Meanwhile a lot of the taxes are going to social assistance programs, but if you're using taxes that tax the people who are the recipients of those benefits, that's entirely counterproductive. You'd be better off removing those taxes and not having those programs than setting up a huge bureaucracy that just takes money from the same people it gives it back to with strings and paperwork attached.

Property tax is one of the more regressive taxes because everyone needs a place to live.

[1] The proponents like to claim that it doesn't distort at all, but you still need the government to accurately value the land, which it can't do perfectly, and if it doesn't then you'll have e.g. land being abandoned because the tax is set too high and exceeds its value. This also creates a perverse government incentive if "abandoned" land goes to the government. Of course, property tax has a different perverse incentive: The local government wants to make housing more expensive so they get more property tax revenue.