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.
I have replied to "What exactly is it about children under the age of 12 that requires a car?", I did not say it is unique to children. But children is a big factor. We did not really needed a car before we had children. Now we need two cars.
"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" is a nice thought, no objections.
So how about we'll talk about "owning a car ... should be considered a luxury" first when "everyone should be able to get everywhere they want to go easily" is implemented? Because it's pretty far from my reality.
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.