If a person is not confident wielding the axe or hachet, it still can be used in the style of an ulu knife. So if it is there, it can be put to use relatively safely.
Someone who is not used to wielding an axe or hachet probably should not pack it anyway.
I probably might have a hachet with me as part of my camping equipment but not as a part of a dedicated survival kit. The points Doug made convinced me a long time ago.
I once received a minor cut when I carried an axe with the flat side of the blade resting on my forearm to gain some manouverability.