Interesting argument here for the 1860 Henry. The definition of Assault Rifle is a select fire weapon, using an intermediate round that's good out to 300 yards (or so). Putting that volume of fire into the hands of individual soldiers changes the entire tactical dynamic down at the squad, platoon, company level. Of course, this presumes that leaders appreciate the advantages of suppression fire and movement that the technology allows, something that wasn't always appreciated in the Civil War. Still, there were enough cavalry units supplied with this and similar rifles (Spencer, for example) that some leaders must have grasped the advantage of the new rifles. Then, after the war, Army Ordnance quickly abandoned all interest and went with the single-shot Trapdoor rifle. In the civilian world, this prejudice didn't exist and the rifle, and later improved lever-action designs, became a staple of the Indian wars, on both sides.