I think it's a cultural thing. Where I'm from I've never seen a parent carry a child's books for them unless they have a really long walk and the books are too heavy. Around here the kids have a backpack and take the bus. Even the kids who live close enough to the school to walk carry their own backpacks.
My middle daughter broke her arm a few weeks ago, so she has a full arm cast on right now.... she is still capable of slinging her backpack over her shoulder.
It isn't a matter of right or wrong so much as culture, individual family, and personal choice. Whatever works best for you. Everyone has different reasons for why they do the things they do.