> That proposition exists as a protection from homeowners being screwed by the government being unfair about the value of their land
According to The Permanent Tax Revolt (https://www.amazon.com/Permanent-Tax-Revolt-Property-Transfo...), Proposition 13 was largely the opposite. Previously, homeowners benefited from informal and corrupt tax assessments that lagged market values. After assessment practices were modernized and standardized, homeowners demanded protection from the market. And while many states created protections (e.g. low-income circuit breakers, elderly exemptions, and homeowner exemptions), California’s Proposition 13 protections (along with the later Proposition 58/193 hereditary privileges) are probably the most regressive among the states.
> does property tax really even make sense? This person PURCHASED the land but still has to owe the government taxes even though they own it?
Yes, a property tax (particularly, on the unearned portion which is the land value) makes sense as a progressive way to enable the fruits of the community to be used to benefit the community. For one thing, a private owner should not reap all the benefits from the economic activity around him that he did not earn. For another thing, private ownership should not last forever because that leads to concentration of wealth; one could similarly ask whether copyright and patents should last forever.
> Secondly, it is really important to think of real estate as an investment more than a physical asset. These people got in the market early and their investment is giving them great returns. I think that is fair.
I disagree. The economic justification for investing in capital is that investors help to make the country more productive. Driving up the price of land does the opposite; investment in land crowds out investment in capital. The value of land comes from the neighborhood’s economic activity and public investments, not from the individual landowner. Now, you could argue that giving the landowner some incentive will encourage more civic-minded engagement, but I think it’s a far cry from justifying giving him 100% of the increase in ground rents.
For a recent book on the moral foundations of land ownership, I recommend Rethinking the Economics of Land and Housing by Josh Ryan-Collins, Toby Lloyd, Laurie Macfarlane (https://www.amazon.com/Rethinking-Economics-Land-Housing-Rya...)