While you bring up additional issues -- I don't believe you can dismiss the fraud in EBT programs. North Carolina has at least 8% fraud in Food Stamps as announced by our state HHS department. Other states have far higher percentages.
At this point I can support limiting the ability of EBT to not pay for luxury foods; however I cannot support limiting EBT to not pay for "junk" food. The reason for this is that some children will tend to not eat if "junk" food is not part of the menu. The easiest example of this is when school lunch programs went to only providing "healthy" choices (thanks Michelle) then most of the food in the cafeteria went into the garbage. Kids want to eat pizza and things they enjoy, not someone else's concept of healthy food.
Limiting EBT to some third party's definition of healthy food will be work just as good as not feeding the kids at all.
The best way in my opinion to move low income households towards healthy foods is to provide deep discount coupons for healthy items (with the rebates effectively being provided by the food mfg/distributors) as part of the EBT program when purchased with an EBT card. Also provide additional awards each quarter for buying some level of healthy items with an EBT (cash or something).
You're surely just trolling now?