Traditional methods could be hand rubbing (like in India or Nepal), or dry sifting on silk screens (like in Lebanon, Morocco, Afghanistan, etc). I would only prefer it as a cultural or historical experience, to better understand how it is used or has been used around the world. And also to help better understand how plants are selected in those areas and what impact that has on the kind of hash they produce. Smoking hash is still quite enjoyable, but I wouldn’t necessarily choose it for every day consumption over rosin.
From my experience, dry sift makes the best quality hash, but it is a very low yield. Water/ice hash is somewhere in between, with medium yield and quality. Dry ice hash includes the entire trichome stems, so you will notice that it doesn’t form together as well. For this reason, I think that is why it is the lowest quality, and not because of other chlorophyll containing plant material, which you can easily separate by grading. When you press rosin, it doesn’t matter if you have only the heads or the heads and stems. In both cases, the non-resinous parts are mostly bound inside a matrix of plant matter and kept inside the press bag.