People endless discuss the merits of solo hiking versus hiking with a group, usually accepting that membership in a goup is somehow safer.

Well, there are groups and then there are groups. An assemblage of individuals is not necessarily a group, certainly not in the sense that a group can respond effectively to emergencies, communicate, and cooperate productively.

To answer your question, one hikes with an ice axe because it looks cool. It is also pretty effective at digging cat holes.