My point with the hiring people to sort it, is that the cost of hiring people is the true cost to the public in needing to sort it. It is that much labor.
Truthfully, it is even more labor to do it at home, since at home it is done inefficiently unlike how it would be done at a sorting facility. Also, at home, it is done by citizens who are professionals and businessmen whose time is more expensive than the workers who would do it.