Despite rent-seeking being undesirable for purposes of equality, more people rent-seeking over more houses does mean more competition in the rental market, and

Despite rent-seeking being undesirable for purposes of equality, more people rent-seeking over more houses does mean more competition in the rental market, and you'd expect rental prices to go down as a result. If you want to eliminate rent-seeking and have low housing costs, the only solution is an appropriate land value tax plus sufficient construction. You can't have affordability with insufficient construction, supply is a prerequisite.