I don't see how that's unique to children, all sorts of life situations require spacial responsibilities. I could write the same thing about my own medical appointments and I don't have children whereas my grandparents had ten (10) children and never owned a car in their lives.

The original thought was "everyone should be able to get everywhere they want to go easily without owning a car so a personal automobile should be considered a luxury." You're describing a situation where the first criteria was not met so the second, of course, won't follow. So your situation doesn't apply and it doesn't take away from the original idea.