I think this calculus becomes slightly different when you're talking about a nation that will never be in an existential defensive war. A protracted war benefits no one, but knowing that a war would be protracted might benefit the side that would otherwise be the loser by serving as a deterrent to the winner.
A protracted war benefits the military of the weaker side but I doubt their people would like it. Also, I can't recall the last time the United States was deterred from entering war because it would last too long.
