re: What is the purpose of buying insurance on a rental car if you have your own?

If you read that rental agreement, you are probably agreeing to pay for damages immediately (and lost revenue every day the car isn't rentable, possibly), not tie it up years while the insurance companies figure out subrogation and who's going to pay what.

If you total their car, are you liquid enough to make them whole right now and wait until the insurance companies figure out what they're not going to pay and then fight them to get the difference between what you paid and what insurance claims they'll pay?

There's part of your answer.

It's a moot point, though. OT ballers don't rent. We buy a new limo when we're in a strange city and just give it to the chauffeur when we're done with it.