Of course in this case it would have been trivially solved by the city just adding sidewalks, but that feels like another point here

It sounds like the family lives just outside of city limits of a small town, so a sidewalk or trail would involve significant investment for the benefit of very few people. I think in this instance its not actually an infrastructure problem but simply a challenge of where some people choose to live.

When you choose to live outside of town you're specifically choosing to always drive everywhere, and to receive no city services at all, and you're subjecting your kids who lack the same freedoms that you do to the same choices. Plenty of people choose the individualism of not receiving city services in exchange for being alone in the woods

As much as I'd love a world where everyone has a sidewalk, once you're out in the sticks it just becomes really hard to make sense to put a trail or sidewalk there. Especially because even if you imagine a world where every town is connected together by a dedicated cycle trail, said trail would ideally not run directly parallel to the noisy highway