This is what sold me on suppressors. I watched from a hilltop as a friend snuck down a brushy creek bottom going into a field to get within 200 yards of a herd of elk that were feeding there. When the herd bull finally came in to the field and started scent checking cows, he shot. From the hilltop we watched the bull drop, only heard the crack of the bullet breaking the sound barrier, no boom. The rest of the heard just stood there nervously milling around, looking at the dead bull. (normally they would have stampeded out of that field). As they started to leave the field, walking and occasionally stopping to look back at the field, he shot again and filled his cow tag. This would not have been possible without the suppressor. I've had the same type of experience multiple times since then with elk and deer.
The hearing protection it provides is an added benefit as I have never worn hearing protection while hunting (always wear hearing protection at the range, even when shooting suppressed).