Most cars that left the road were the oldest and heaviest. New cars bought under that program tended to be economy cars and are already a decade+ old. To suggest that it took inventory off the road affecting today's markets doesn't hold water.
The biggest issue is that car companies make more money off reselling the loan than they do off the car. Years ago we tried to buy a Subaru in the NYC metro area in all cash and were continuously turned away. Dealers didn't make money off the cash sale, they were spiff'ed off the loan. We had to take the loan and then pay it off in order to get the car.
Since then it's gotten worse. Expensive cars (luxury, trucks) are sold with 72 month loans and are underwater shortly after purchase. It's been a race to the worst terms and empowering the worst purchases to the worse equipped buyers. I'm continuously amazed it's gone on as long as it has.