Yes, that's completely true. But while there are still inputs for which terrible accuracy could result, for many of the inputs which would arise in practice, th

Yes, that's completely true. But while there are still inputs for which terrible accuracy could result, for many of the inputs which would arise in practice, the Kahan summation technique is "good enough" to prevent loss of accuracy. The chances of getting an input for which catastrophic cancellation would result on the doubled precision are far overshadowed by the chances of getting inputs for which the normal summation would have unacceptable loss accuracy, but Kahan summation would not.