Your thought process is almost correct. The restriction against frangible ammunition was meant to make war more "humane" by making rounds that either 1) killed the combatant out right OR 2) Allowed for wounded to be cared for.
The main goal of war from "modern" times up to mid-20th century is to distroy the enemies ability to make war, not to necessarily kill or to punish the enemy combatants. Repairing someone who has been hit with fragmenting ammo is a difficult job. In the 20th century few armies were up to the task. This meant that combatants with non-fatal hits with fragmenting ammo ended up suffering slow painful deaths. It was felt that there was no reason to "torture" the enemy, just get them out of combat -- so if they do not die, let them be patched up and send home. If you are shot clean through the body with an FMJ your not going to be coming back to battle soon anyway.
In big game, wounding and repairing is not an option, a clean hole through is more torture for an animal who cannot get treatment, and a frangible round has a greater potential of killing outright.
That was definitely the theory at the time against a modern, conventional army that has a value on human life. Look at us, we have dedicated medevac helicopters, field hospitals, advanced trauma kits at the squad level, etc all to save a man.
Extremists hold little to no value on human life and won't stop to try to save their wounded like we do. Hell, they strap bombs to their own guys to try to wound or maim. Anymore, we need something that stops the threat as soon as possible, not wound and let their buddies stop to take care of them.