Since they are formed by parts of the die breaking off, it seems intuitive that they would be edgy and sharp at least in places. What is the metallurgy of the die itself?
Die chips are often not smooth. However, metal can break off in smooth patterns, but also keep in mind, that with die chips and especially cuds, the break can be too deep to make an imprint on the planchet. The metal gets pulled up into the incuse area of the die, but not far enough for a detailed transfer of the topography of the surface of the break.
Notice the smooth nature of the underside of this die fragment which was amazingly found with the coin- http://www.ngccoin.com/news/ViewArticle.aspx?IDArticle=3185&print=1
I suppose ... even in that example the die part edge looks sharp but the cud edge looks smooth. Makes you wonder how we get sharp details on coins.