why did Napoleonic war soldier's wear hat instead of helmets? Watch
Then during the first WW armies switch back to issuing helmets. So why did helmet fell out of fashion in the 1750-1850s?
Most cavarly formations, also prefered fighting without any armor, because the loss of speed, nimbleness and stamina, would be too great if armors were to protect from firearms of that era. Even armies that relied on armoured cavalry for a very long time, swiched to light cavalry that didn't use any armor, because their historical shieldings became useless by the mid XVIIIth century. In fight against enemy cavalry, it was more reasonable to be more nimble, and preserve strenght, while in a fight against infatry, it was more reasonable to get in sabers' effective range, before the infantry manages to fire another salvo.
Helmets were re-introduced during WWI as protection of face from shrapnels exloding in the air, that were ejecting low-velocity particles, that could massacre soldier's face, and knock him out, however steel helmets could protect from those low-velocity particles, while they still couldn't stop the bullets.
Also, production of helmets was expensive, and Napoleonic wars were already wars of the masses.
Another thing that helmets wouldn't be much of a use for meele combat, because such was not considered a viable tactic at that time.
The war tactis was quite extraordinary- it wasn't about hand to hand fight or destroying the enemy by any means possible. The point was to use strategy and tactics, to put your forces into a situation when your highly disciplinned army could scare the enemy off. That's why infantry was steadily marching to music, when attacking, instead of running at enemy.
The point was to break the nerves of the enemy soldiers and make them run away, before the distance would shorten to fist fight.
This is also why WWI was such a bloody massacre and continuous stalemate. The old generals were trained in XIXth century tactics, when battles were won through the display of morale, and underestimated the power of modern fast-reload cannons and machineguns.