The North and the South needed the their form of the conscription act for opposite reasons.
The war was popular in the South all the way up to the fall of Atlanta. The problem retaining troops was not the mission, rather for the South the problem with troop retention was just being in the Confederate Army because it was so arduous, feast or famine food, maybe decent uniforms maybe not, and strict disciplinarian generals that loved to fight but cared little about the day to day running of armies. The Southern Quartermaster corps was corrupt and "sutlers" were never allowed in to relieve shortages and provide a few things to make camp life bearable.
The problem for the North was the war was not really popular. The Union had all the supplies it needed and compared to the South camp life was a vacation. Sutlers, "Hookers" and supplies were plentiful. Discipline was lighter than the South. There were a few times the Union had supply problems but that was on purpose as a tactical move they chose to break of and go without supply lines, like the "Sherman's March". There are other examples of where Union Armies were cut off (Nashville and Mississippi Campaign) but those are the exceptions.
So the war was unpopular in the North and the mission unclear. First, the war was to "preserve the union". Then, after losing battle after battle, they switched to freeing the slaves which went over like a led balloon. Draft riots and conscription soon followed.
Then why the need to enact conscription in 1862 and forcibly extend all enlistments for the duration of the war? Something Lincoln never dreamed of doing?
The problem retaining troops was not the mission, rather for the South the problem with troop retention was just being in the Confederate Army because it was so arduous, feast or famine food, maybe decent uniforms maybe not, and strict disciplinarian generals that loved to fight but cared little about the day to day running of armies.
So they were willing to fight but not willing to put up with hardships? Really? I imagine if faced with a Valley Forge the Confederate army would have deserted on day one, huh?
The problem for the North was the war was not really popular.
And yet the Union army remained overwhelmingly powerful throughout the war. The army could have faded away in the spring and summer of 1864 when the three year enlistments ran out. It didn't because the overwhelming majority of the troops reenlisted to see the war through to its successful conclusion.
Speaking of Confederate troops:
“I know that this country without slave labor would be wholly worthless, a barren waste and desolate plain— We can only live & exist by this species of labor; and hence I am willing to continue the fight to the last.”
Captain William Nugent, writing to his wife from headquarters, 28th Mississippi Cavalry, Tupelo Mississippi on September 7, 1863