A property tax is a wealth tax.
It is a relic of a time when all property was held as a trust of the king. The idea of "private" property was just bizarre. In the United States, only property owners could vote. So the tax responsibility reflected the political power property owners wielded.
But now we DO hold the liberty definition of property, the Castle doctrine ("a man's home is his..."), and we have universal suffrage. We continue to tax property now, largely because we always have. That said, it's a bizarre, inequitable tax because -- even though the rich tend to own or rent more expensive property, it is still a brutal tax on the middle incomes. And we all know that government is averse to taxes that impinge significantly on the middle incomes.
A tougher question, given our acceptance of property tax, is the wealth tax. Why do we tax the accumulated wealth of people only in the form of the theoretical value of land and structures but not in the form of stocks, bonds, and savings accounts?
The answer to that is that liquid capital can go elsewhere. Property cannot. Taxing liquid wealth means that people will station that wealth elsewhere and stop stationing locally. That will have an impact on many other economic behaviors that the governments DO tax. So it is consistently understood as a bad idea. Not that governments don't engage in misguided tax schemes. But since the leaders in a representational Republic are typically just the sort of people with the most to lose to such a tax, they are highly attuned to its downsides. And the middle incomes are not the idiots that political scientists seem to assume. They see potential trouble in a system where a tax system is imposed and maintained by the people very people with the most to lose by it. It just looks like a pre-assembled dumpster fire.
This reminds me of GK Chesterton's Fence. He said that if you find a fence in the middle of the woods with no apparent use, your first inclination would be to tear it down. But he argued that that is a risky mistake. He said that you ought to first understand what caused someone to build that fence in the first place so you can know if it is safe to tear it down. It was an argument in favor of "conservatism" is social policies.
In short, the just because you can see an injustice does not mean that it is best to figure out how to eradicate the injustice. Sometimes it is better to allow it rather than make it illegal or abolish it -- while keeping in mind that it is STILL an injustice; because that might warn us against creating new injustices. Private property seems to produce more overall good than Feudalism. Taxes and government are compulsory and unjust. Well, sometimes, life is like that. Sometimes, the agonies we suffer are actually the best of all possible worlds.