There is no reason not make it universal. A lot of kids will still bring their own lunches. Teens in high school will choose paid lunch options some of time. The program would probably have a similar cost to SNAP.
Hungry kids don't learn well, so feeding them will lead to a modest increase of academic achievement on average. Academic achievement correlates with higher earnings, thereby paying for the program with their future taxes.
>>megama+(OP)
This seems to make sense on the surface, but I'm skeptical about the last part. It seems we're in a race to the bottom and "good" jobs are increasingly scarce. It seems there aren't enough good jobs for the population. Basically, the logic you laid out is probably sound for small marginal changes, but I'm skeptical it would scale well due to the competition and limited resources.