Renters insurance protects the landlord from liability claims. They don't care if you insure your own property, but I don't know of an insurance company that decouples liability and property.

Also, renters insurance is cheap, I haven't rented in more than a decade but when I rented I was only paying less than $100/year for it.

I just looked it up and currently the average premium for renters insurance is $15 to $22 a month.