There is a kind without the... screw, the spiral thing I mean. It's pointy and just slightly curved in S. I've been unable to find an image for it in five minutes.
I bet that, once you get used to it (after spoling a few hundreds of corks, that's it) it's faster than the "rabbit" model.
I say that because I used to be faster with the simple, T-shaped screw, and I've seen it used in restaurants by experienced waiters.
In a similar note, we have a "rabbit" corkscrew. It's super efficient at opening a bottle, but is not particularly satisfying. Have you ever asked yourself, If only I could open this bottle faster? (Although it can be convenient if you're cooking with wine.)