Yes. They had. From ancient times we have very little sources, but about the Romans we have, and Grossman uses their accounts to support his case.
Romans observed the tendency to slash instead of stab both in their own soldiers and the barbarians, they also recognized the superior effectiveness of stabbing. The one thing they didn't know what makes people rather slash than stab, what is the psychological reason that works behind, so that they didn't write about. But their recruits went through rigorous training to come over the preventing block, and enable them to stab, and to make that into habit.
Beside in OP, I also mentioned Romans here: >>8961
At both places I note the role of officers who encouraged, pressured their subordinates to kill.
Besides the uniformity of their soldiers (everyone had the same equipment, arms, responsibilities, rights, compensations, etc) and the "job" done together alleviated the individual guilt over killing, made it more bearable by sharing it with each other. Doing the job well was also rewarded, and instilled a contempt against their adversaries, deny their humanity by labeling them inferior ("barbarian").
So to sum up, training, "psychology", teamwork, and the pressure of an authority was used by the Romans to be better killers on the battlefields than their enemies. They met problems with enemies (eg. Persians) who had a technical filter between the killer and the victim (eg. horse archers) and had superior posturing techniques (eg. cataphracts), but as long as they could keep the quality of the legions, they were a match. When Romans started to rely on troops which didn't have the training, the mindset, didn't have officer corps, then started the real problems.