I am agreeing that the shots you describe are possible. I am also agreeing they happened. I doubt that they were a major part of firing.
Do you have accounts of formed bodies firing in this manner? If not, then we can consider this to be a firing method employed by skirmishers.
Let us consider the firing power that a French infantry battalion of 600 men might generate. Allow 1 peloton in 6 as skirmishers, is 100 skirmishers. Typically one half of the skirmishing peloton was in reserve, so that would be 50 men actually firing. Let's also assume that the enemy's skirmishers are leaving the French skirmishers alone, therefore the French can fire at will (I am considering the anecdote you offer from the artillery officer as an example. Then let's assume a rate of fire of one round per minute. That would indicate 50 rounds per minute sent in this arcing fire. What proportion might actually impact the target area from 1000 paces or about 800m? Having fired a lot at that range, even with modern weapons, I can suggest only a small proportion of such arcing fire. Let's be generous and suggest that 10% of such shots would hit a person. That would be a hit rate of 5 per minute. Then as Decker says "contusion ... which causes little damage".
So this analysis gives an upper bound on hits
I think that a 10% Probability of hit is ridiculously high, by an order of magnitude. So, if we consider a hit rate of 1%, then one person in the target receives a contusion every two minutes.
That sounds highly unproductive against anything but green troops or those who have never seen such long distance firing.
I must admit that I find this quote from Templehoff: "A small arms ball kills or wounded a man as long as it hits regardless of being short in an arc or horizontally" to be problematic. First, it conflicts with other accounts, which assert that arcing fire rarely kills. Second, my analysis of the ballistics of a round with no remaining forward vector, and therefore only having the downwards vector imposed by gravity, is that the velocity is limited by height, and that it is further limited to the terminal velocity defined by the mass, shape and surface area. It is my view that the velocity of a musket ball at extreme range would certainly be enough to cause a contusion, but very doubtful to cause an injury leading to death, or even an injury sever enough to keep most soldiers out of the line.
So if I consider the effectiveness of such fire to be minimal, why would it be used? For the same reasons that ineffective fire is used today and has been used through out history. Such fire harasses. It may intimidate. It could interfere with rest. Every now and then a shot gets really lucky. Perhaps most importantly, it gives the firers something to do, keeping them busy and improving their morale.
Now let's consider that Templehoff is actually suggesting that a formed line would start firing at 600 paces. Unless the unit was highly trained, it is doubtful that even 1 in 100 rounds would hit the enemy. Let's allow 2 rounds a minutes rate of fire. Even at that we are talking about 12 hits a minute from a battalion of 600. This hit rate would increase as the attacker approached, assuming the powder smoke did not obscure visibility. It would require approximately 8 minutes for infantry to advance 600 paces, implying 100 casualties give or take. Lethality increases at closer range. Weapons failures increase with prolonged fire. Visibility also decreases with such fire, reducing accuracy.
As a benchmark, if we compare this to the preferred British approach of reserving fire, if we allow that one in 10 shots had effect at 50 paces, then the first volley would cause 60 casualties, and a second volley at even closer range at least as many. It is worth noting that the total hits in the two firing approaches are similar.
It would be interesting to try and quantify all the different approaches to defensive fire and attempt to correlate them with different armies over time. I think the only one for which there is common agreement is the British reliance on withholding fire to achieve a damaging volley at close range.