Sure, but taxes are applied due to political feasibility, not because they "make sense".
The most sensible approach is to tax natural resources (land, carbon, mines, wells, electromagnetic spectrum) and other forms of economic rent, but that is politically infeasible (edit: or more accurately, very challenging) in a capitalist democracy.
From an economic standpoint, the most "sensible" (i.e. most efficient and least distortionary) tax is one that relies primarily on natural resources and other forms of economic rent instead of taxing labor, businesses, non-land property, wealth, or the creation of value. However, these rent-based taxes would need to be set very high to fully replace income, corporate, payroll, sales, property, VAT, wealth, estate, etc taxes.
Switching to such a system would be painful for people whose net worth is disproportionately invested in land or who consume significant resources relative to their income. If the majority of the population fall into this category (as is not uncommon in capitalist democracies) then such taxes would be broadly unpopular, making them politically infeasible.
It’s more accurate to say it it’s politically infeasible in our capitalist oligarchy.
Just because this is the way our society works now, we shouldn’t be duped into thinking this is the natural order of things. It’s not. A democratic society with a free market economy could work very differently.
But I'm not sure I agree that the difficulty is due to being an oligarchy. In a democracy where the majority of citizens have the majority of their capital tied up in land (as is the case in the US and many capitalist democracies), shifting the tax burden onto land seems like it would be broadly unpopular.
I do agree with your main point though that a democratic society with a free market economy could work very differently, it's really the transition that would be broadly unpopular, and therefore politically difficult in a democracy.