While free parking is appealing for many users, it’s definitely not for many others because unlike Airbnb, the value of their possession (in this case, their car) is variable while the compensation (free parking and $10/day rented out) is fixed in the sense that it is pre-determined.
With Airbnb, the compensation is variable and is set based on the owner's perceived value (which factors in the 'emotional piece of mind’ too among other things). It’s essentially a market based approach, and to get a wider acceptance from the supply-side, that’s what FlightCar needs to incorporate while preserving simplicity.
As an optimist, I believe the creases will get ironed out eventually. It’s not going to be easy (never is) and it might take some time, but it will happen. Here’s a structure that comes to my mind:
Tier 1 – Free parking and $10 for every day the car is rented out (like they have now)
Tier 2 – Pay $X per day to park and Receive $Y for every day the car is rented out, where X is the market rate which in SFO’s case is $18 and Y is the daily rental-price you name.
While I think this is a good approach, since the service's main drawbacks involve cosmetic damage, it makes sense to launch using a payment model which favors lower-end cars. Once the damage issues are adequately addressed in practice Tier 2, or an equivalent, might become more attractive.