Various sources I've seen credit edged weapons with 15-20% of the casualties in the European line infantry era. For instance:
1715 Paris Invalides records for wounded men:
Infantry small arms: 71.4%
Swords: 15.8%
Artillery: 10%
Bayonets: 2.8%
Source: John Lynn, "Giant of the Grand Siecle: The French Army, 1610–1715", 1997, p. 489
1762 Paris Invalides records for wounded men:
Infantry small arms: 68.8%
Swords: 14.7%
Artillery: 13.4%
Bayonets: 2.4%
Source: John Muir, "Tactics and the Experience of Battle in the Age of Napoleon", 1996, p. 46 (both this and Lynn's seem to reference the same source, Corvisier)
European and American casualties in wars from 1800 to 1850:
Infantry small arms: 30-40%
Artillery: 40-50%
Edged weapons: 15-20%
Source: Trevor Dupuy, "Handbook on Ground Forces Attrition in Modern Warfare", 1986, p. 55
On top of that, pistols and shell splinters would also account for some, folded into the greater "small arms" and "artillery" categories. I mention these classes of threat in particular because they're all things that well-made plate armor could potentially protect one against, as detailed quite well in Alan Williams' "The Knight and the Blast Furnace" chapter 9.4. Contemporary military thinkers were clearly aware of this, as heavy cavalrymen ("cuirassiers") continued to be infrequently issued plate armor even in the mid to late 19th centuries, beyond the era where it was actually useful.
My question is this: why was this limited solely to some cavalrymen? I can see why it might be too expensive or troublesome to give to every grunt. But why was it not issued to shock troopers like grenadiers, who were expected to get into hand-to-hand combat with some frequency (hence why they, unlike the common infantry, were issued swords and sometimes grenades alongside their bayonets)? Or to garrison troops in towns, who (by contemporary observations) got into hand-to-hand combat far more frequently than men in the open field? Or even to all cavalrymen, whose primary role involved close combat with pistols and swords (and occasionally lances and axes)? By the early 17th century munitions plate was cheap and mass-produced to the extent you could outfit every grunt in it if you wanted to, and technology only improved as the centuries went on. Was it purely an issue of weight and comfort (a well-made cuirass is about 20 pounds)?
Did anyone even think to do this? Were arguments made for or against it at the time? It just seems odd to me that even in armies that heavily emphasized close combat, like the Swedish Caroleans, keeping plate armor for select infantry never seemed to be considered except as a fashion statement for some officers. Even in WWI, when it would have been far less useful, some shock troopers wore breastplates.
Cuirasses are hot and heavy. Yes, 20 pounds doesn’t sound like a lot. But when you have to haul it dozens of kilometers a day on the march, it suddenly becomes a much bigger issue. They also retain heat really well, as a result of their metal construction. This, of course, presents serious problems, as your average infantryman only has his canteen, and can’t exactly drop out of the line to go grab more. Even without the heat of a cuirass a man could faint from the heat, as many did at battles like Monmouth in the American Revolution.
Along with this, the reality is that a Cuirass really isn’t going to stop a musket ball, especially at the ranges these weapons are being fired at. Even if the ball itself doesn’t penetrate, the shock of the impact will no doubt do serious damage to the man it hits. At the bare minimum, it’ll knock him out of line, and that’s ultimately the goal of a Napoleonic battle.
Battles in the Napoleonic era were not fought to the last man, at least not except in rare cases. The goal was first and foremost to shatter the cohesion of your enemy, because once the enemy can’t properly fire volleys, the damage they can deal goes down immensely. A unit with Cuirasses and a unit without will have their cohesion shattered all the same if they take a few enemy salvoes. Will some more of them be alive? Quite possibly. But the unit will still be rendered ineffective, and that’s what matters when it comes to winning a battle.
In conclusion, a unit with a Cuirasses would be slower, more prone to heat, and just as likely to shatter when hit. Would they have a higher survival rate? Probably, but that comes at the cost of being no better, or even worse, at the things that are expected of an infantry unit.
The primary reason Cavalry continued to use them is that in the Napoleonic era, Cavalry primarily fought other Cavalry. These weren’t sporting those heavy muskets that could so easily punch through a breastplate, they instead were facing down pistols and sabres, weapons that a Cuirass was far better at staving off. Though, when a cavalry unit was expected to fight infantry, such as a Dragoon or Lancer unit, they often dropped this cumbersome armor piece and went into battle dressed more like an infantryman.