I throw jabs and crosses with horizontal fist and hook with the vertical.
There are two issues at question:
1) How to punch to avoid hand injuries?
I am convinced, as are many others, that using the middle of the fist as the point of impact results in fewer hand injuries than using the first two knuckles. Dempsey believed this as well. I think it is true regardless of whether you throw horizontal or vertical punches.
2) What is the most effective punch for speed, power and accuracy?
In Dempsey's time (and pre Queensberry) most fighters believed the most powerful punch to be vertical fist. See this 1891 article in Outing magazine for relevant pictures and text.
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Boxers of that era also often threw punches from the waist, or even lower. Check out this Dempsey highlights for examples
Jack Dempsey highlight by Liu Jin . They did a lot of other things no modern coach would teach including throwing straight punches with the vertical fist.
Looping punches such as hooks derive their power from hip and lower body action, what Dempsey called "shoulder whirl". Dempsey had a brawling infighters style and threw a lot a hooks and other looping shots, having notably one of the best left hooks in history.
Other fighters that throw looping shots use the vertical fist with good effect. Chuck Liddell uses looping hooks and overhand rights that frequently land with the vertical fist. De La Hoya, another notorious hooker, throws looping vertical fist shots including a deadly vertical fist style shovel hook he calls his ".45". Tyson is a classic example, there are others.
Straight punches, the jab and the cross, benefit from twist and the horizontal fist. Twist creates "snap", can cause cuts in competition, and results in more power because it recruits the muscles in the top of the shoulder that otherwise are unused.
Orthodox out fighters that rely on jabs and crosses, which is most of us, will get more power and effectiveness out of straight punches thrown with the horizontal fist.
Boxing moved to this style of punching not long after Dempsey's time. It was the result of having hundreds of fighters hitting things (bags) and people and discovering it was more effective.
It isn't that vertical fist doesn't work, its just that it isn't the best tool for the job if you are talking about jabs and crosses and the "JKD Lead Punch" is just a muthafuggin (pre-1920) jab by another name.