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.
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.
