stone tools like hand axes were not well suited for combat. For example, war clubs the dominant weapon of choice in every stone age culture I know of, despite using hand axes for work and spears for hunting.
IMO any culture that participated regularly in warfare would have figured out that sharp spears with long reach are far more effective than clubs unless that combat was largely symbolic. Clubs would make sense because they're not as lethal.
[1] https://link.springer.com/article/10.1007/s12110-023-09445-3