Is Additional Insured on Renter's Insurance Necessary?

[Dave Bopp]

A current tenant acquired a renter's insurance policy that listed him and his girlfriend on the policy as the insured individuals. He asked the insurance company to have the landlord added as an additional insured and the insurance company told him he could only have two names on the policy. 

How important is the additional insured on the policy? Should I require the tenant to terminate the policy that he's paid for to find another company that will allow them to list their landlord as an additional insured?

Thank you!