And yet present day hunter gatherer societies tend to have extremely strict gender roles. For example the idea of a woman going on a hunt is not taboo, but simply unthinkable, maybe similar to what we would think about a man taking lactose pills to breastfeed. At least that is what I read in Sabine Kugler's excellent books. So somehow I doubt everyone participated in everything.

Selection bias. Notice how most present day groups are in hot and relatively stable climates, areas where one can hunt/gather all year. Look to past groups in the north where seasonal changes meant the window for any particular food source was always limited. When there is only a short window, it is maximum effort from everyone.

The same is true for agriculture. Even today, with all of our mechanical wizardry, farmers on the plains still pull their kids out of school to help during harvest.