That never occurred to me, but now it makes perfect sense.
Something like 20-30% of households get the average lower middle class amount for groceries per person (30/month per person, $120 per person per month, $500/month for a family of four). SNAP isn’t intended to be the whole amount they spend on food, simply a large share. Hence the “supplemental”, with an incentive to work part time or make other money to buy more and better food.
There are a disproportionate number of families that don’t manage the money, blow it all by mid-month and hit food banks by the end of the month.
And all of that money is supplemented by free school lunches and breakfasts for the kids, WIC for infants, etc.