"dealer [...] was entirely befuddled by the concept of paying cash"
I guess they get higher commissions if they tie you into some profitable (for them) financial deal.
When buying my last one, the dealer tried in every possible way to persuade me into some kind of financing, just nothing was really below 7%, and I really had no investment delivering more than that (probably I should enter that market too), while paying cash was no issue. At least I got a discount, my father buying a different brand didn't even got it.
It's quite clear with such interests rate it's a big advantage for them to make you pay the car more - it's another of the many ways money are transferred from the base of the pyramid to the top without much effort, just luring people into buying something they can't afford.
Just like when they give you for free credit cards... with big interest rates on debts made. They act like drug dealers.
I prefer to save and then buy only what I can afford, unless really forced to do otherwise, and anyway, minimizing any outstanding debt.