This but make it progressive over the total value owned. Corporate or trust ownership structures etc pay top rate to prevent obfuscation.

Someone owning an investment property to help fund retirement seems reasonable. Someone owning thousands does little for society and likely hurts it.

LVT doesn't have to be progressive to make land hoarding unprofitable. It just needs to be appropriately proportional to land value.

The problem that the progressive tax solves is allowing small scale landlords while stopping large companies. An equal tax means that a person with an extra home they are renting out is just as unprofitable (or even more so, because of scale) as a large company.

As mentioned by topkai22 above, this might not actually be a problem, and is desired in some places.

Why is that a problem to be solved to go socratic about it?

A single extra home rental being less profitable will exist "naturally" as a matter of economies of scale essentially with fixed cost component redundancy.

Income inequality and imbalance of market influence (if one person owns 90% of real estate their high level of control can't even be called disproportionate because they actually do have that large of a stake) seem like issues better addressed by straightforward income taxation and antitrust respectively.

Why not progressive over total wealth or income, as opposed to restricting to just land holdings?