One of course being don't rent yours out. Obviously there would be insurance included in rental fees to cover the costs of that. While I would be opposed to mandatory ID for rental (you don't need ID to take a Taxi after all) one could still have non-linked rental cards (filled with cash) which have a reputation, and you could agree to rent only to people of a certain reputation. People would no reputation would be limited to renting "system" cars with higher insurance rates.

The wealthy would probably not rent out their cars at all, or perhaps rent them only to 'clubs' of trusted people. But that's still a lot better than today, when our cars sit in garages almost all the time, doing nothing and using garage space. Others, who could never afford to buy a car for themselves, could do so by being willing to rent, and take the risk.