I’d imagine the main benefit of downpayments to be behavioral, since otherwise the borrower has no stake in the asset initially.

I doubt that's the main driver for lenders and people are generally pretty attached to and excited about their new cars. They also do have a stake they'll still be out time and money even if insurance covered the entire cost of the vehicle.

I wasn’t really thinking about people wrecking their cars, but rather about making future payments.

Losing the use of a car and your equity in it to repossession is much worse than losing somebody else’s car alone.