Again a safety net for those who need it but not for those who can afford it.
So far fewer kids take school meals, including fewer of those who are eligible for free school meals (possibly because all their mates aren't having school lunches or something). So the current situation is worse at providing a safety net for those who need it. And the kids who need it were the ones who benefited most from this.
The position on what is provided for kids at schools and what is brought in is essentially arbitrary. Most people would assume that books were provided in schools, but on the face of it, there is no real reason why books (essential for learning) are provided, when food (essential for learning) isn't. There's no reason parents who can afford to shouldn't pay for their kid's reading books. Basically there isn't a real moral reason for parents to pay for some things and not for others, it is just how society happens to have evolved.
So personally I think we should just treat this as the same as any other spending on educational or health interventions; rather than take some kind of moral stance on the rights and wrongs of giving people food, we should look at the improvement in outcomes from it versus the cost, and judge it on that. Looking at the study, it at least rules out the obvious 'make the safety net a little bit bigger' approach to free school meals, leaving you with two choices, keep the current approach, or free meals for all, depending on whether you think the learning improvements in the pilot studies suggest that it is worthwhile to spend that amount of money.