For one, the story could not really exist as it is if it were told from Jerry's mother's first-person perspective. Because she is clearly unaware of the dangerous choices Jerry is making when she's not with him, the story would not include his time with the older boys, practicing, or actually swimming through the tunnel. It would likely just focus on her own anxieties as she sits on the "safe beach."
If, however, the story were told from Jerry's first-person perspective, then we would lose, most importantly, all the references to what his mother is thinking as well as what the older boys think when he joins them in the "wild bay." Because her internal conflict is helpful to our understanding of where Jerry is in his maturation and development, we would miss the majority of that context if we were unable to know her feelings and fears. We might even condemn her for her choice to allow a child who seems so incapable of making good decisions independently to leave her sight. Further, it helps us to see how the older boys view him as well, to know pretty clearly how they interpret his childish antics.