This was an ongoing problem with musket armed soldiery; in the Peninsular and Napoleonic wars, in-experienced infantry often shot high, and given that Brown Bess was the standard musket for the British Army from 1722, presumably an issue at least since then.
As such I am doubtful whether the sights of Springfield rifles are a key factor in this problem!
At a guess I would pin responsibility on two factors:
1) If you don't allow for it, the recoil of a musket will tend to kick the muzzle upwards - an experienced soldier can ride the recoil and control it reasonably well, but inexperienced troops are likely to let it rise.
If the muzzle kicks upwards, the bullet will go higher than you expected, and so inexperienced soldiers are likely to shoot high. This is going to be exacerbated by the twin facts that many armies did not practice musketry with live ammunition on cost grounds, and that even those which did usually practiced volley fire only, not target shooting, so there was no clear way to gain knowledge that you were shooting high before engaging in combat.
2) The unwillingness of most soldiers to personally kill when they do not feel immediately threatened.
As researched more recently (an article reporting on it can be found here, most soldiers looking over their sights at a human being not already trying to kill them will feel a strong impulse to aim off, or close their eyes when shooting to give the guy a chance, or similar.
Assuming this phenomenon held true 200 years ago, and I see no reason it should not, the most sensible way for a soldier standing in line, facing a line of enemies to his front, to deliberately miss is to aim up. If, however, all of his mates are keeping their weapons fairly low, aiming at chests or stomachs of the opposing line, he will look very obvious if he aims above their heads! So getting the whole formation to aim low could be a way of using social pressure to overcome the unwillingness to actually aim directly at enemy soldiers, and thus make more of your volley hit.