Great comments so far. The above caught my eye though.
I think when we are talking about human flesh a blade being "not that sharp" does not add much of a safety factor, if any. Especially if it is being used properly. This gets exponentially worse if the blade we are talking about is a sword. I recently did some tameshigiri training under the guidance of a Japanese Kendo Yudansha. I was able to cut cleanly through a target with a dull iaito, a strike which the Yudansha indicated would cut cleanly through a human wrist. I was quite shocked to hear that proper power placed behind a dull weapon could have this effect.
Luckily the attacks used with "not that sharp" blades are not attacks aimed to kill, but a slip with a "not that sharp" blade has potential for severe damage.
Just my 2 cents.
Just to chime in on this aspect... Draw-cut swords do not need to be razor sharp to cut and do serious damage. My customers all want to have "scary" sharp blades and that's cool if the target being cut is soft, wet tatami. But the best cutting blades are vastly more than just the edge and edge angle. One I did recently for a senior instructor in a sword style. Yes, it was sharp. But the overall geometry was very traditional and he was quite surprised at how well it cut on a variety of targets, even feeling better than thinner blade he owned that were "supposed" to be the sharpest stuff out there. The reasons are complex, but the overall cross section of the blade plays an enormous roll in all of this. And people have been seriously injured with "unsharp" iaito including deep cuts. A well performed cutting motion with even a dull blade can have devastating consequences.
I walked out of a demo one day because the sensei kept grabbing the tanto (apparently a live but dull blade) with his bare hand on the blade and over the edge. I would love to see him do that with any real tanto with a decent edge. Just a quick tug on the blade and he would be looking at a handful of stitches. I just couldn't watch.