I am extremely skeptical that the few vacant lots are enough to counterbalance what would essentially be a massive tax break for every new homebuyer.

I'm in favor of everyone paying taxes fairly to get high quality city services, instead of having people with large increases in property value getting an unfair tax subsidy.

This brings things back to taxation of realized vs unrealized gains. If you want fair Taxes, we should probably do away with property tax entirely, and focus more on income taxes themselves.

The people with the most wealth tend to pay much less (proportionally) in income tax. Most people find this unfair.

I don't think that is true. The bottom half generally pays zero income tax. The proportional income tax increases continuously. There is no group that makes more and pays less proportionally if you look at the actual data. Here is the percent income paid (after all deductions) for different groups.

You can always argue that the proportion should be even higher, but the proportion of income is certainly not lower

https://www.cato.org/blog/federal-tax-changes-1979

People that are wealthy enough don't really pay income tax.

For example, one loophole during the ZIRP era was that one could get a very low interest rate loan (<1% APR, so effectively lower than inflation) against appreciated securities and use that money tax free. If the wealthy person passes away and gives the appreciated securities to their heirs, their heirs have a step-up cost basis which is the market value at the time of transfer, so no taxes are ever paid on the appreciation of the stock. The heirs could then turn around and settle the loan, tax free, as their cost basis matches the market value.

Warren Buffet famously pays taxes at a lower rate than his secretary.

https://abcnews.go.com/blogs/business/2012/01/warren-buffett...

This is an anecdote but there's no reason to expect that this doesn't apply to his classmates.

So, yes; given all the rebates and loopholes and shenanigans that the rich and mega-rich can use, the proportion of income is lower.

Then you don't know the real estate speculation game. Investors buy vacant plots at the periphery of a city for cheap and just... wait. When it is time to sprawl you have to pay huge sums to them for land that is empty. The tax break that you think is going to the home buyer merely raises the value of this land and the investor is getting the money instead of the local government that managed the city.