From what I know (and it is theoretical), the hammering 'draws' out the edge. If you didn't hammer, then continued sharpening would, after a while, result in a thick sickle edge. Sickles are used for cutting very thin and fragile stuff, so you need a similarly thin edge (just like you use a thin edge for shaving). So the peening draws out the edge, the sharpening with the sand does make for a 'saw tooth' sharpened edge like you said that is good for a slicing cut.
Billhooks are for chopping much thicker stuff, hence need the thick convex edge, not dissimilar to a splitting axe edge in profile. Most of the time you use them on green wood so they won't need sharpening very often.
Billhooks are for chopping much thicker stuff, hence need the thick convex edge, not dissimilar to a splitting axe edge in profile. Most of the time you use them on green wood so they won't need sharpening very often.