Keeping in mind that Tolkien's studies and inspiration was anglo-saxon culture. His model was a chieftain. They were purely leaders of their families and would go into war leading their troops, proving themselves worthy to hold the title.
It is not tribal, rather it is the clan system, with chieftains and a "high chief" or king.
Thinking this, it makes sense why the kings would go to war with their men along with thier heirs would go out and to war or to quest. Legolas was mentioned to be possibly be related to Thranduil, as a prince. Lego had yo go out and prove his right to be heir.
Though I suppose what I just said summed up several other comments that have already been given.
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Mes sana in corpec sano- (lt.) A sound mind in a sound body
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