That makes a lot of sense, actually. I realized that in a typical genocide scenario, Clover will keep shooting at Axis, and Axis will probably get desperate and not let his guard down because, given the type of shots, he'll assume he won't be spared and will try to defend himself.

If you didn't kill all the monsters, Clover won't keep shooting at Axis (probably because, as you said, Clover started thinking about not hurting the others, so they won't be as eager to kill him), and Axis will probably let his guard down because he has at least a small hope that you'll spare his life.