I think a better question is what percent of the average person's net worth is tied up in the unimproved value of their land? I posit that unless they are pretty wealthy, it is nearly nothing.
This is a good representation of how housing (and therefore land) is valued: https://twitter.com/bufordsharkley/status/138799739507868467...
The tax incidence from a land value tax on someone living in a 300k home in rural California is nearly nothing, while it will be massive on a wealthy person living on a $5m home in Palo Alto. Their actual physical homes are fairly similar - the 4.7m difference is land value. I don't see why it isn't progressive. You give an unrepresentative example of literally the wealthiest person in the world - what about for 99.9% of people? Sure, it isn't literally the most progressive tax possible, but you can apply your argument to the progressive income tax we have today. Jeff pays literally 0 income tax, but that doesn't mean in general the income tax is not progressive.
If you are that concerned about it being progressive - and not the efficiency benefits of the tax - you can literally just make it progressive. 0% on the first $X/ft value of the land, 10% on the next $Y/ft, etc. This would solve your problem with farms as well (if you are not convinced by the graphic that 1000sqft in SF is worth more than 100 acres in Idaho anyway).
The world's richest man own $500m of real estate. Sounds like a lot until you realise it's 0.25% of his net worth (and the unimproved land value's possibly sub 0.1%)
What percentage of the average American's net worth is tied up in the footprint of their home? Guess it's two orders of magnitude more than Jeff's, and potentially >90% of the value of the average farm. Hence not remotely progressive, even if it's less worse than a pure property tax in most circumstances and other even more regressive taxes.
> As far as I understand, the vast majority of the farms are on rural land that has an unimproved value of close to zero. I don't see how they would pay much taxes.
It takes a lot of land to make a farm. (Sure, per acre it's less than the city, but city dwellers don't own many acres and unlike the farmer have a realistic proposition of selling their limited acreage to a condo developer when the tax makes it unaffordable).
c.f. It takes zero land to make a much higher margin SaaS startup.