We should expand it and repeal income taxes and prop 13.
But really, Prop 13 is among the most ham-fisted damaging legislation you could possibly point to...
(1) initiatives which are exercises of legislative power reserved by the people to adopt a law initiated by citizen petition,
(2) referenda which are exercises of legislative power reserved by the people to approve or reject measures passed by the legislature, either with the assent of or over the veto of the governor.
(3) legislation referred to the people by the legislature (often because it would impact a previously passed initiative statute in a manner which the legislature has not been delegated the power to do without popular assent.)
Prop 13 of 1978 (proposition numbers get reused, so “Prop 13” alone is technically, though only rarely practically, ambiguous—though confusion from that ambiguity has been suggested to have helped the defeat of Prop 13/2020, which was on the ballot with two measures that would have modified Prop 13/1978, Prop 15/2020 [which failed] and Prop 19/2020 [which passed]), specifically is an initiative constitutional amendment.
Taxes are a matter of choice - a (democratic, even vaguely) society makes a choice to spend a certain amount of money, and as a reflection of that, they levy taxes on a variety of things to raise something roughly equal to that amount of money. These taxes will affect different people differently, and they will affect different kinds of income and different kinds of wealth differently. Some taxes are based on what a person is paid for their labor. Some taxes are based on a person's ownership of something valuable. Some taxes are based on what a person spends. What matters is who pays what and why, not whether "the money was already taxed".
But you're right that we have a choice in whether or not we levy a tax on the ownership of land/buildings. Personally, I'm more a Georgeist in such things, and I think that taxing the ownership of land is an excellent idea, much better than taxing income or spending. But I don't feel that Georgism itself answers the question of how to determine how much tax a person would/should pay for owning a particular piece of land.
I suspect you don't believe that there can be society-wide collective goals, and I just don't have any time for that nonsense. I spent too much of the 90s on Usenet arguing with people who thought that, and it just isn't worth my time anymore.
The reason property taxes are based on value is that it acts to tax wealthier people at a higher rate than poorer people. Plus, just because the money that purchased the land was taxed means nothing to the local community. Sure, the federal & state governments have already taxed that income, but that means nothing to the local community, who has to pay for schools and EMS every year. And these services act to make the property more valuable, so why shouldn't the residents of the community pay for them?
1. There are places in the civilized world without property taxes.
2. I am not proposing a regressive tax system, I am proposing a tax system based on actual consumption and frugal mindset. People are always equal until they are not - one man one vote is good, but one man one dollar tax is bad, 'cause some men cannot afford to pay for the services they get, but they have equal right to vote. That is hypocrisy. In some circumstances I am fine with people living on state care or UBI, but they should completely give up their right to vote as they are incapable of having a solid life for themselves, so they are incapable of deciding for community.
3. When you pay per service, you are a lot more careful with what you ask for and what you get for than when you pay a sum for a bucket of "something". A colleague that lived somewhere in a small town in Ohio told me they did not have a police force in their community by choice: the cost-benefit ratio was not good. A different colleague told me she was paying about half of her salary (low level manager in a big company) as property tax for the small farm her family had for generations, somewhere in West Virginia. In my part of the world most of the tax money are wasted on things that are not necessarily the biggest priority for the community, but the politicians are rarely competent and most people don't mind the waste, while others like me do. This is why I am looking at a zero tax and pay per service to eliminate waste.
In a progressive tax system, the burden of taxes is related to the marginal utility of money. That is, an extra $1000 for a person who earns $15k a year has enormous utility, whereas an extra $1000 for a person who earns $150k a year is of much less utility (and this trends to zero utility as base-line income rises).
Consequently, when you collect $1000 in taxes from a person who earns $15k, you have a dramatic impact on their life. When you collect $1000 in taxes from a person who earns $500k a year, it has very littl eimpact on their life.
This notion of "progressivity" in taxes has been at the heart of most taxation in most western nations, including the USA, for centuries.
Your suggestion does not follow this, and is thus called "regressive" - people are taxed without attention to the marginal utility of money.
And BTW, there are some cafes/restaurants (not many, but a few) that do offer progressive pricing.
If the taxes get locked in, then you get the "2 neighbors with near identical houses paying totally different amounts in taxes" problem.
If the taxes are not locked in, then you get the retired lifelong home-owner (or renter) on a fixed income, unable to afford the increasing taxes (or rents).