The whole thing to realize here is that the 'cost' is not an actual loss as in 'less money comes in'; it's a cost in the sense of 'this portfolio will perform less than we anticipated'. And if the interest that people pay is based on a certain overall performance, but now all of a sudden the performance needs to be adjusted downwards, then one might argue 'we were shooting for a 0-operation, but in the end we will have to spend money to make up for the good borrowers leaving'.
Here's another intuition that explains it: if the market is willing to finance the good borrowers at half the rate it takes to lend to everybody, regardless of their prospects of paying back; then only the bad borrowers will stay in the government-funded portfolio, reducing the performance that was originally estimated. Which is, if you've accounted for future earnings based on the original estimate, a loss when you have to write it down.