It still seems like that would save a ton of unpleasant work, if not time.

I own a pasta machine where I have to hand-feed the pasta sheets, and it's so much easier and more fun to make pasta compared to rolling by hand, even though it doesn't save me any time.

Simply feeding an item into a wringer is easy and a bit meditative; wringing by hand is a lot of work and a lot of wear on your skin.