Yes, fisticuffs were common for impromptu human fights. But the stuff with evolutionary implications usually resulted from ambushes: People hiding in the bushes with sticks and stones, waiting for one and his buddies to walk by.

Or just hitting him over the head with a rock while he slept.

Forager societies more closely resemble middle school than modern life. In modern life, you can get in a fight at the bar and not see the person you lost to for weeks - if ever. In middle school, you lose a fight and you have to see that person every day for the rest of your life - unless you skip town (leave the tribe) - which appears to have been somewhat common.

Thus any fisticuffs victory will be hollow, as the loser can simply murder you one day when you least expect it.