With the installment payments. Surprised the other solution is so widespread.
From the state's perspective it makes sense, it means they collect the entirety of the tax even if the loanee defaults. It also allows them to collect the entire tax on items bought through "trade up" programs. I work for a cell phone carrier, hence my familiarity with this, basically many today in the US at least offer plans where once you pay off a certain percentage of the phone's total value you can trade in the phone and get a new one. If tax isn't collected up front then the state only gets a tax on the percentage paid for the item, not the entire value.
But it's a pain when buying a car.