"Rich kids would eat free too" is actually a good thing for the following reasons:
1. Reduces stigma for those who need the program.
2. Reduces cost and limits bureaucratic waste when the entry bar for the program is streamlined
3. There are very few actual rich kids; there are kids with rich parents. And not all of those are as loving and attentive as they should be.
4. Rich kids are still kids. All kids should eat.
@Lana point 1 is so very important in my view. It should be easy to recoup from richer users through the tax system if only we would use taxation more progressively!