As I mentioned, Illinois (and I assume some other states) charges soda and candy at a different tax rate than groceries. This hasn't led to some state-wide chaos of determining what the tax rate of caramel apples should be or thrown the tax code into disarray over flavored water. They decided "soda and candy get standard taxes" and that was it. It may be "arbitrary" but it's not "ever changing".
This was more or less where my answer came from. I think we touched on this in an earlier thread. In California, they do not charge sales tax on "staple goods". So milk, flour, bread, water, uncooked/prepared food, etc have no sales tax, while everything else does. I don't support a specific targeting of "soda" in this regard, but that anything which isn't a basic food necessity (which soda, fancy bottled water, beer, etc are not) should have a sales tax attached, and thus should not be purchasable with food stamps. Now, I'm not sure if that's actually the case in terms of food stamps here, but I have no problem with it being so.
You're leveraging an already existing system in place. If you've decided that certain things are not necessary and are luxuries, then food stamps should not be used for them. Obviously, in states which don't already have something like this, they'd need to come up with restrictions. But I don't think it should be "ban soda", but "food stamps can only be used for <insert standard here>".