I'm sure we've covered the tactics of the war before but I'll just point out that "neat rows" was actually a fitting strategy and the advent of rifled muskets didn't really change that. Keep in mind that they didn't have radios or any means of communication other than flags, bugles, and drums. So, formations had to be kept relatively close to those giving commands. Also, black powder makes a lot of smoke and after a few volleys the enemy might be pretty hard to see; so not much aiming. Massed troops allowed unit control and for massed fire in the general direction of the enemy. In fact, a number of regiments actually preferred smoothbore muskets and some thought buck and ball the best round. In addition, most troops weren't trained marksmen so even if their muskets had a long range most wouldn't have been able to take advantage of it. The supposed advantages of a rifled musket were also minimized by terrain which was another factor that forced close-range attacks.
Of course, later in the war entrenchment was becoming fairly common and there were sieges. In those cases, aiming and long-range shooting were more typically employed and so it could be argued that the rifle had come of age. Before that, though, the only way to deliver effective firepower while keeping control over the troops was by massing and attacking by company and regiment.
Oh, and things had progressed from Napoleonic tactics so it's not accurate to say that CW generals were fighting exactly as European armies had done "centuries" before. This is seen in the way cavalry was used, how artillery and infantry were coordinated, and the elimination of formations such as the infantry square. The bayonet charge wasn't employed as the standard infantry attack that it had been in earlier European conflicts either (although it was still employed to some degree).
Thus I think it's a mistake to characterize CW commanders as somehow foolish to have used the tactics they did or to say that they were still employing Napoleonic methods. Just my two cents.
I would recommend these references:
Nosworthy, Brent (2003) The Bloody Crucible of Courage: Fighting Methods and Combat Experience of the Civil War (Carrol & Graf Publishers, New York).
Hess, Earl J. (2015) Civil War Infantry Tactics: Training, Combat, And Small-Unit Effectiveness (Louisiana State University Press, Baton Rouge).