Earlier quoted context omitted.
Adding "$1 trillion in student loans to the federal balance sheet over a decade" is a result of direct lending, ie cutting out the middleman. It is also saving the taxpayer money to the tune of $70B over ten years.
It doesn't save the taxpayers any money if the government makes foolish loans that can't be repaid that nobody would have ever lent out if their own money was on the hook instead, nor does it save the taxpayers any money if the government provides easy, free money that causes unnaturally skyrocketing tuition followed by an unnatural higher ed crash. An awfully expensive $70B over ten years, I think.
The savings of $70B comes from eliminating a profit layer that was enjoyed by the banks.
The government insured the loans before and after the change in 2010. So the taxpayer was on the hook for losses. Now it is still on the hook for losses, but also benefits from profits.
The $70B is simply from cutting out the middleman.