I know the repeating rifle was available in the mid 1800s. However from my understanding the bolt action rifle was the weapon of choice in WW1.
The repeating rifle can be reloaded without taking your hands to far from the trigger whereas the bolt action certainly requires moving your hand away from the trigger.
It just seems that the repeating rifle could have been more effective but faded from popularity.
Lever repeated rifles such as the Henry and the Winchester had a few flaws that made the armies of the world choose the bolt action system.
First of all, it is hard to repeat with a lever action while lying down. Secondly, having the repeating mechanism open downwards creates problems with moisture and mud entering the system and causing problems for the repeating mechanism. Thirdly, most bolt action rifles could also be loaded from above with stripper clips, allowing for a faster reload.
The finger on the trigger is a moot point, as the repeating action would throw the rifle off its aim anyway - the soldier would need to re-sight his rifle anyway.