War is about the killing. How effective at the killing.
Mosin was more effective at killing than any rifle before the smokeless powder age.
In terms of range, accuracy and sheer murder on the target. And it can do so quicker.
It goes back to the Dreyse v Lorenz or Garand v Type 99 in that firepower is key. A few more rounds per minute per gun may sound like pennies but when multiplied it gives one side the edge.
So in the civil war we have to look at an average soldier with his weapon. Not the outliers. So if the average rifle was the 1861 then he is shooting 2-3 rounds per minute and probably closer to 2 as the battle progress. In the British army, pre ww1 the British infantryman was to shoot 15 rounds per minute.
So 100 infantry armed with 1861 may or may not fire 300 rounds but the British army 100 infantry are going to shoot 1,500 rounds in a minute. It's not the same. Not the same sport. The Mosin is a craptastic rifle but I would still expect 10 rounds aimed shots at the very least. And at longer ranges too.
There are guys who can ring a bell at 500 meters with a Mosin like er...ringing a bell. And this is all weather day or night. Just ain't the same sport.
In some ways you are right, it is about the killing.
While the Civil war rifles (or Crimean war) weren't much faster in rate of fire to the older smooth bores they had around three to five times the effective range.
Which meant you could shoot at attackers for 3 to 5 times longer before they reached you with a bayonet. So if you could inflict 3-5 times the casualties before the bayonet charge reached the defenders (if they reached the defenders at all) you had a huge increase in combat capability.
This was what
should have changed the tactics of the 1600s,1700s and early 1800s.
But it didn't.
It also really changed the value of infantry vs cavalry. In the ACW many cavalry units fought as "mounted rifles". that is they used the horses for increased mobility to let the unit gain a favorable firing position rather that try to fight from the saddle with sword, pistol and lance in close combat.
The increase in the rate of fire of the breech loading rifles just made things worse.
And the Breechloading rifles also increased their effective range even more than the muzzle loading rifles.
Turkish troops were causing casualties among the Russians at over 1000yds in 1877. Granted the Russians gave them a great target as they marched up the roads in column formation up to 10 rows wide and hundreds long and those large lead bullets hitting anywhere in that mass of men was dangerous.
The Turks only their Winchesters when the ranges got to around 200 yds or less.
Again, small colonial wars often reinforced the wrong lessons, (closely packed squares of European troops shooting up spear armed natives didn't advance infantry tactics)
and European generals derided the ACW as armed mobs and likewise ignored some of the lessons of even the Boer war.