My background: I've run a car rental company for nearly 7 years now, so I know a thing or two about the logistics. Granted, my business deals with luxury/exotic cars, so some of the issues we face are quite different, but nonethless the core issues remain.
Here are my concerns:
* Rental cars get treated like crap, whether it's a Buick or a Bentley. "Mystery damage" appears in a high percentage of rentals. The customer will, 9 times out of 10, say "Oh, that was there when I picked the car up." We solve that problem by having a trained staff member take photographs of the car before and after and have the customer sign a very detailed check-in and check-out report with every inch of the car covered. In the event of a dispute, we are documented up the wazoo. If these transactions are happening person-to-person, how is that documentation being done? It takes at least a few weeks of solid training to get our employees accustomed to having "the eye" for damage to our cars. I doubt P2P renters are going to train themselves. This, then, opens up every rental experience to a massive potential for liability and dispute, and in the cases where the documentation isn't up to spec, both parties will be left with a very bad taste in their mouths (and potential lawsuits).
* Insurance. They claim to offer insurance, and I'm sure they've managed to find a carrier to cover them, but insurance in the car rental world is dicey at best. Often carriers will provide coverage, but if you've got too many claims (and a business like this is ripe for claims -- see above) then you'll get dropped like a hot potato. And if you get dropped, there aren't many other options. And the few options that exist cost 2x - 10x the price. I've seen this again and again - it's very easy to start and run a car rental company for the first year. Then you have an accident and it comes time for renewal and the story -- and numbers -- change dramatically.
* In general, and this is my weakest argument, lots of people try to enter the car rental business because they think of cars as commodities that can be treated like any other piece of equipment. The problem is that cars are massive rolling accident and lawsuit machines. If you're renting a dress to someone (Rent The Runway) or your couch (AirBNB) or a watch or a tux or etc. etc. etc. that's one thing. But there isn't a chance that dress is going to cause a death. Or a massive accident. And if the dress gets ripped, it's a $100/$1000 problem, not a $20,000 or $50,000 problem (or in the event of an accident w/ injuries, a $20M problem).
Anyway, I want to embrace new and innovative models, but this smells of disaster to me.