The LVT isn’t a tax.
It is a compensatory payment for the opportunity loss of those excluded from valuable locations, by those wishing to exclude them.
Saying it is random, is like saying paying rent is random. Or paying peoples wages is random.
The capitalised value of slaves fell to zero when people had to start paying wages. That wasn’t an anti-lottery. That was just compensation, just like LVT.
We don’t have a perfect market. It has deadweight losses due to the imputation of rent and the excessive inequality property rights in land bakes in. The LVT makes the market perfect.