“My aim” is not to reduce inequality. It is to have an economy free of distortions so that it can allocate resources to those able to put them to their best use. That maximises wealth and welfare for everyone in the long term.
As I’ve already explained, if those excluded from valuable natural resources are not compensated for their loss, then not only are those resources not optimally allocated but excessive inequality is baked in (because unlike labour/capital, land is irreproducible. Which is why this is specific to Land). Both of which cause a (net)deadweight loss.
This has nothing to do with the government renting out land. Land is not contingent upon humans for its existance. So no one and nothing can have a property right over it. We should only expect to be compensated when we are excluded from its use as this is fair and optimally efficient.
That is the rationale for LVT.