Thanks for the interesting article.

Even though most of the casualties were caused by musket and artillery fire, the bayonet was tactically very important in Napoleonic warfare. A bayonet charge is absolutely terrifying, and the reason why there were relatively few casualties from them is likely because soldiers would break rank and flee in the face of one. If soldiers had stood their ground and fought, casualties would have been much higher, and with their low rate of fire, muskets would have been of little use in hand-to-hand combat.

They key change that happened in the mid-1800s is that firearms finally achieved ranges and rates of fire that made closing with a massed enemy nearly impossible.

I suspect running into grapeshot was a tad more terrifying than a bayonet charge.