Currently the PRS charges the maximum it possibly can, because its purpose is to make landlords as much profit as possible. Without competition driving down prices, PRS rents will continue to spiral upwards.
By making the social sector compete directly with the PRS, it will apply a braking force to this upward spiral. As the social sector reinvests its revenue into more housing provision, it will reverse the balance between PRS and social housing.
Ultimately in any market the provider with the keenest prices and the lowest operating costs will tend to dominate, so by bringing a not-for-profit sector into direct competition with the for-profit sector, the not-for-profit sector should ultimately win out and become dominant.
Meanwhile, the needs of those on low incomes who cannot afford to pay the going rate for accommodation should have assistance provided through the benefits system.
That would ensure that everyone who needs help gets it, but those who don't need taxpayer subsidy don't receive it. Everyone would be equal - no stigma associated with living in social housing any more, no price differentials for social tenants to exploit by subletting their homes at elevated rents for profit.