Presumably we could come up with some sort of middle ground policy. For example, there could be certain foods that are excluded from the system or maybe only certain products are included. Or perhaps different products could use up more of a person's "food credits".
This is basically Cuba's policy (well, Cuba in better times, their rationed food has decreased massively in quantity over time). Everyone has an allotment of basic staples (rice, beans, limited meat, coffee, etc.) that covers your basics with little / no extravagance, or you can go to a grocery store for a wider variety.
I think you wouldn't need to actually do any work to get this effect. Consider what happens if tons of people suddenly decides to take home a particular "fancy" food for free. The government pays the grocery store, but the grocery store also runs out of the food and buys more from its supplier. This is driving up demand for the fancy food. Now the fancy food is going to get more expensive, even though people are getting it "for free."
If you take my sibling comment about tax effects into account, this means that, as people over-consume a "free" food, and its price rises, they're effectively making larger and larger "purchases" which will have an effect on their taxes.
On the other hand, if it turns out that the food was only expensive because few people were buying it, in a sort of vicious circle—then when everyone buys it, and forces demand up, it'll force supply up, too, and the food will get cheaper for everyone, not just for people who get it "for free."
For example, if it turns out that we only weren't factory-farming caviar because of the low demand, but it's perfectly possible to do so, then we'll just turn into a society that farms and eats a lot of cheap caviar. No market distortion; just "unlocking" market efficiencies we couldn't previously reach, because the demand side didn't previously have the dollars to vote with. Everybody wins!
this seems needlessly complicated. it would be a neverending game of whack-a-mole to get the whitelists / credit multipliers adjusted for every food sku.
if we're already assuming people can budget reasonably well, why not go with a UBI-like food stipend and enroll every citizen? calibrate it so people with zero income get a reasonable (possible COL-adjusted) amount to afford a month's worth of healthy meals and phase it out smoothly respective to income. can't really be abused unless you hide your income and also avoids the fiscal cliff.