That also seemed pretty silly, as they hadn't had that much experience of war. I think there may have been some before the actual War of the Shadow, but not enough so that Demandred would have far more experience than anyone from the third age.
We also know that he was basically lazy, and that despite being a child prodigy and gaining the third name, he never fulfilled the early promise. It seems unlikely that he would have put in the time and effort to become an expert swordsman.