I can park at Park SFO for $10/day. Off-airport parking at other airports is generally similar.
My car costs me about $0.25/mile ex-fuel to operate (depreciation, maintenance). That's pretty standard; for a new car, it's easily more than that.
I value my time after arriving back from a long flight at $100-200/hr (in general I don't, but in the specific case where I'm exhausted, I do). That's why I drive to the airport, so I have my car waiting for me on arrival. If I didn't, I'd just take BART (and sometimes do).
At 90 miles/day mileage limit, I lose money ($22.50) if someone rents my car, even including free parking ($10) and the rental payment ($10). If I leave my car parked for a month and no one rents it, I'm ahead for sure (the cost of parking). If I had a car with only legal minimum liability insurance and someone destroys it, I'm also probably ahead based on their liability policy (I hope).
Speeding/red light/etc. stuff would be totally obnoxious.
The hassle of having to remove everything from the interior of the car, trunk, etc. and then replacing it after, as well as documenting condition pre and post rental, and any dropoff/pickup hassle vs. the Park SFO or SFO Long-Term Parking options, pretty much kills it for me anyway, but those aren't universal, so I'm not including those. Maybe some people value the free car wash more than the hassle of those things.
The only way this would really make sense for me vs. parking would be if the payment were substantially higher, OR if you got some non-cash benefit for renting out your car -- such as cheap/free rental of an equivalent vehicle elsewhere. I can sometimes get awesome cars from Hertz for $20-30/day, but in other cases, it's $100. Being able to "trade" my car for an equivalent car in another city at little or no marginal cash cost would be compelling. The cars could be other customer cars, but could also be from car dealers trying to demo/sell new models or something.