I suspect those having to move to benefits will have issues with their agency or landlord
How would they even know? With universal credit, it goes straight into your bank and you pay your rent.
It's different for new tenants, because they have to pass credit checks, produce bank statements etc, but if you're already in a tenancy, I really can't see how they'd know.
And with the mortgages, the Council of Mortgage Lenders agreed to allow a payment holiday, so it's not totally the government's decision. They have no powers to force landlords to allow a rent holiday, and there's no regulatory body for landlords, so I can't see how the government could make this happen, tbh.