The only thing inevitable will be that eventually Land-Value taxes will not be enough (if implemented) and then what? There is no end or limit to the amount of money a Government can squander.
Also https://en.wikipedia.org/wiki/Henry_George_theorem shows "that under certain conditions [presumably including limited squandering, though I didn't check], beneficial investments in public goods will increase aggregate land rents by at least as much as the investments cost"
The government can also hand out cash raised from the LVT as a UBI.
Problem solved.
It's a flow of income (land rent) that can accrue either to everybody and be shared or to individuals. One way or another some party has to be the beneficiary. The question is who deserves this unearned income?
On the other hand, certain parts of the political spectrum are very emphatic about wanting to reduce both budget and expenditures, and sometimes manage to do so.