I had renters insurance whenever I rented. Why?
It covered things like damage to the rental suite -- e.g., if I had (another, ahem) pork rib fire in the over that got out of control next time, lit candle catch curtains, or for those with waterbeds / fish tanks,... kid flushes world's largest rubber toy down toilet, my barbeque catches fire, etc.
It also covered against theft.
When we rented a house, it would cover against the postman slipping on the front step (due to a kid toy or misplaced mat, or something my fault), or provide coverage for a maid (example) injured while completing a home service.
It would cover against trampoline accidents (my trampoline), and if I managed to damage neighbors property (through a water leak, freak gardening accident, ball through a window).
Honestely, though, I was never concerned about a friend suing me for an injury while visiting...(maybe if you own a dog?).. nor about replacing possessions other than theft....