Point is that taxpayers are subsidizing your gain in disposing a car that isn't worth the book value, as well as the process of transporting and selling the car, and KQED might not get much money at all.
What I don’t understand is what prevents a for-profit service that provides hauling, and returns to you the auction proceeds minus hauling fees and zero value insurance. Then car owners would have a real choice between pocketing ~50% of the car value and giving it to charity and getting only ~30% as a tax deduction, and they would be less likely to give the car to an unsavory profiteer.