While it's evident that there was some anachronism in ACW tactics-- what exactly would you have had them do? The Springfield muzzle-loader could still only fire 3 shots per minute-- a thin line would have left them outgunned and vulnerable to a strong enemy advance.
There was a regular application of a thin line in combat-- otherwise known as a skirmish line-- but it had very little staying power, as all the enemy had to do was advance. While it is certainly true that Battle Lines would have been more effective if they would have trained to take cover (as they surprisingly often learned to do!), a full and true evolution in tactics was not feasible until further advances in both range and rate of fire-- and the amorphous lines of today were not even concievable until the introduction of the light machine gun as the Main Fire weapon.
DA
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