They’ll generally accept a cashier’s check. Ours would also accept a personal one as long as you didn’t mind them delaying mailing the title for a few weeks.
I made a down payment on a car with a money order and the dealer yelled at me that the agreement said they weren't allowed. Eventually they relented, because they wanted to complete the deal.
Back in the 90s, I tried to pay for a computer with a certified check and CompUSA treated it as a likely counterfeit.
Yes, was attempting to pay full amount. Couldn't remember my PIN to unfreeze my credit, and just seemed like it would be easier since I was in a position to pay in full.
That makes somewhat more sense. Trading a signed title without a lien for a check places a lot of risk on the dealer. Although there are ways to mitigate this, maybe the dealer in your case didn’t feel like bothering or it didn’t occur to them.