The onions do a couple of things. First, the flavor cannot be compared with plain non-onion latkes. Second, the onions help keep the grated/pureed potatoes from turning brown or gray. Also, keeping the peeled potatoes in cold water prior to processing, helps to keep them white,as well.
I use my processor and pulse a very large onion together with a lot of potatoes (maybe 8-10 large ones. I make it almost pureed, but with a little coarse potato, not totally smooth. I add a few eggs also, and kosher salt and pepper to taste. I avoid flour and matzah meal, because we have a gluten-free member of the family, but if I feel the mixture is too watery, I add in potato starch a little at a time, to get the right consistency. Then I fry the latkes in very hot canola oil on one side until the edges begin to brown, flip over and fry the other side until deep golden brown. Then let them drain on paper toweling in a flat pan, and either serve immediately or keep warm in a low-heated oven.