I agree with the skepticism, I always thought the biggest killer in ancient wars were:
* Infections
* Getting stabbed as you routed
But I don’t understand your logic about the arrows. The width of the line shouldn’t cause some sort of scaling issues. I mean, the army of archers would be limited in the sense that training a ton of archers and making a ton of arrows is expensive, but assuming it is possible to produce and supply that many archers, there’s no reason to think they couldn’t all carry their arrows to the front, right?
Eventually your guys run out of arrows of course, but getting them resupplied after the battle is the same logistics problem that you solved before the battle.
Massed volley requires putting all of your archers in one (or a few) places. The effective maximum range of an archer is something like 500'. If you put your archers at the "wings", they can cover at most 1000' of line; but, even a modest sized army (I'm thinking of a standard Roman Republic field army) will have a mile wide front.
Secondarily, you need to use your (very expensive!) arrows effectively, and it's hard to see over the people in front of you to shoot someone in the distance. That means, practically, archers are just shooting the soldiers in front of them — soldiers in the nearest 100' or so. That'd only cover 3–500' of line. (This practical consideration was noted by my Military History teacher from his direct observation of battles in Africa.)
* Infections
* Getting stabbed as you routed
But I don’t understand your logic about the arrows. The width of the line shouldn’t cause some sort of scaling issues. I mean, the army of archers would be limited in the sense that training a ton of archers and making a ton of arrows is expensive, but assuming it is possible to produce and supply that many archers, there’s no reason to think they couldn’t all carry their arrows to the front, right?
Eventually your guys run out of arrows of course, but getting them resupplied after the battle is the same logistics problem that you solved before the battle.