Cutting mechanics are an incredibly important element of practice and performance with the longsword. Without sufficiently good cutting mechanics, techniques that manage to hit the opponent will probably not have any effect on the target, and may end up being more of a slap or a gentle caress than an actual cut.
The Zwerhaw is a technique that is so central to the German martial arts of the 15th and 16th centuries, and yet, so often, I see people training the Zwerhaw in a way that is either ineffective against a cutting medium or only works when they are not wearing protective gloves. There are of course plenty of different ways that the Zwerhaw can be done effectively, but the focus has to be on achieving an effective and functional outcome, and not just mimicking the illustrations or following the instructions superficially.