During a certain period of time (e.g. American Revolutionary War, US Civil War), soldiers lined up across from each other and fired guns in turns. Why was this considered effective battle strategy?

More can always be said, of course, but I commend to your attention the appropriate section of the FAQ, specifically the headers 'Why did European armies use Linear Tactics?' and 'Mechanics of Linear Tactics'.

Adding onto that section, a few more posts:

u/StoryWonker has an overview of the relevant factors;
u/dandan_noodles looks at the dimensions of combat;
and on the degree of risk and likelihood of lethality;
and in conjunction with u/PartyMoses, the relative risks of being in formation;
PartyMoses also covers the dimensions of combat;
also how the fighting should go, according to one contemporary theory;
and on a common idea, why the troops don't duck/get down/lie down/similar.