It is true that a LVT will have a larger percentage impact on the market value of undeveloped land who bought land for speculation without any investments in making the land more valuable. This will especially affect people who bought up lots of land speculating on the value going up. This includes people who bought up lots of land for farm/lumber/mining, but also people who buy up urban plots and keep them as a flat land parking lot while waiting for the value to go up.
Any change in taxes will have some winners and some losers. For example an increase in traditional property taxes hurts anyone who bought expensive houses. An sales tax/consumption taxes hurts anyone who saved up financial assets. An increase in income taxes hurts people who invested in education to increase their labor value.
The question is which is the least unfair way to tax to meet the needs of society. Most of those other taxes will actively discourage valuable investments that make society as a whole more prosperous. Property taxes discourage building. Wealth taxes discourage saving. Income taxes discourage earning and investment towards future earning. In contrast a tax on land value, doesn't cause there to be any less land. It does discourage speculation in future increases in land value, but that speculation is mostly zero sum (it might make the individual speculator richer, but doesn't increase the wealth of society as a whole).
Yes, but you could also say:
"They key is that it is a tax on the relationships between specific landowners and the local representatives and lobby dollars spent"
Now, if you're a farmer on the edge of Austin, and the city's growth means your land is getting increasingly valuable due to high housing demand, then your tax will go up, potentially until you're forced to give up farming and sell to developers. That's intentional, it means the land will be used for something more valuable than it's current use.
It's a fair concern, but also because property tax already includes some land tax it's not dramatically different. Those activities are already mostly done in areas where land is extremely cheap.
The long answer requires a discussion about what you define as "fair" & the exact implementation of the tax governing the land you're talking about. This would be true of any tax though. The answer would still likely be no, though.
Many places have implemented an LVT. I suggest you look into some of them to see how the tax usually plays out in practice. In NSW, Australia, for example, farmland is exempt.
If you are sitting on land that is more valuable than the use you put it to, maybe you should have an incentive to put it to more valuable use?
Land right next to Lincoln is likely to be valued like other residential and industrial spaces; land out in McPherson County is likely to continue to be valued like other farmland.