As the landlord, you want them to have the policy because of the liability. You could care less if they can replace their television. The liability is what's important to you. If they forget something on the stove and cause a fire, their insurance will pay first and yours will be secondary.
seems to me that should be exactly what the insurance is for .. but I really don't know.
I am going to get a copy of a renter's insurance policy from my agent so i can read it.
I haven't been enforcing the clause that they obtain and keep insurance but that is at the top of my priority list of things to do ... make them get it, reword my lease to say if they don't pay at renewal I will and charge it to them.