Agency referencing fees

Now that the government is making agent fees illegal I wonder if we can find a better way to weed out tenants who are ineligible or unable to pay rent but still ask to view properties.
Would it be OK to ask applicants to pay a third party referencing agency to provide a reference and proof of residency eligibility they can show to agents or landlords?
This would avoid the accusation that agents are profiteering and save landlords all training to become immigration experts.