Surely it’s possible that a family might value education but not have the literal time, if they are working non stop, to take the kids to a further school? Or to take care of them afterward?

You’re avoiding the point by saying “anyone who cares can,” and avoiding the economics entirely.

Economics can force choices against your own best interests. If you have an hour between shifts and the school is 45 minutes away, you may have no choice.

This is separate from groups of people who don’t value education. This is about where others make that choice for them.