A few years ago, I called a hand-Matza bakery, and the owner told me that most of the kneading of the dough is done by Goyim. He told me that most every hand-Matza bakery does this. A Jew starts the process by pouring water on the flour, which is considered the start of the kneading process (BTW for that reason assur on Shabbat). He said that he cannot get frum Jews to that kind of hard labor for $10/hour. He tried to hire frum high school kids, but they quit within a couple days.
At that rate, I’m not sure why hand is better than machine.