A substantial down payment serves as a hedge against rapid depreciation. In the first year of ownership, a vehicle's market value drops significantly as it transitions from "new" to "used" status. Without a minimum 15-20% down payment, the borrower is almost certainly in a position of negative equity.
Beyond equity protection, the down payment reduces the total amount financed, which in turn reduces the total interest paid. It also signals lower risk to the underwriter, which can lead to a lower interest rate offer. For those with marginal credit, a larger down payment is often the only way to secure an approval without predatory rates.
Consider the "opportunity cost" as well. While putting money down reduces debt, that same capital could be invested elsewhere. However, in a high-interest environment where auto loans exceed 7%, the guaranteed "return" of avoiding that interest usually outweighs conservative market investments.