If a power station opens next door and price drops, you pay less tax
If LVT is subject to arbitrary changes outside of precise terms negotiated during the initial auction (which should cover the annual cost plus cost increase schedule).
Ultimately, nothing will incentivize the improvement of the value of the property as much as owning the property. I think it's apparent that total infrastructure development would go down significantly under this system, even if there are other advantages. We can minimize risk by including length of lease in the auction, but if there is a maximum lease length, the end part of that lease will always be devoid of infrastructure improvements.
There should be a much more active market in land (land would change hands much more frequently because it doesn't make sense to hold as an investment), which then makes it easy to assess land value.
> And if you risk other people pricing you out of property you currently hold a lease for (especially because they think the value is going up because of your investments in it) I can't imagine that would encourage any development at all.
You're discouraged from building more than you need on land you can barely afford, and in an area that's rapidly changing you're encouraged to build things that you can either easily move, or sell on to future buyer of the land. The intent isn't to encourage development for development's sake, and the result might be less development in areas that are rapidly changing.
This concern is usually addressed by ditching the distorting effects of the periodic auction and of the incentive to try to "steal" capital improvements by abandoning the auction framework and just assessing a yearly property tax proportional to the value of the underlying land were it unimproved. Since ownership and sale of land would still exist in this system, the value of the land for assessing land value tax can be determined by the market value of the land.
If the concern is that poor people might be unable to afford to stay in their homes, why not target poverty or house prices directly rather than adjusting the tax?