Lots of folks are right on about the privilege that's necessary to cook and eat in a frugal way (cooking supplies, storage space, time, knowledge, access to less expensive stores). I used to work helping clients apply for food assistance programs, so here's my perspective based on that:
I think the core of this issue is really that yes, some people can get by on a lot less than $200/month for food, but the allotment has to be the same for every person - big or small appetite, homeless or housed, with a host of complex food allergies or without. Sure, your family of four can get by on half of $668/month, but what about a former client of mine, a single mom who is working two minimum-wage jobs and has 3 kids, two of whom have celiac disease? The SNAP program has to provide an allotment for real people in a wide range of situations with a wide range of food needs and capabilities.
And this is why GuitarStv's suggestion is impractical: people's food needs just vary too widely. There are programs that follow that approach, including most food pantries and the Commodity Supplemental Food Program (which is for seniors, mainly), but they are not generally someone's primary source of food assistance. There is a lot of waste that occurs with that type of program (because, e.g., there was a big block of cheese given to someone who is lactose intolerant, or who is ill and can't have solid foods, or who is a Chinese immigrant and does not know how to cook with cheese). Also, if people on food assistance do not routinely go to the grocery store and purchase food, that raises additional problems: it is yet another barrier to going off of food assistance (because in some neighborhoods, you'd end up with a generation of children who don't know how to shop at a grocery store), and it would probably cause many of the grocery stores in poorer neighborhoods to close, making food access that much more difficult for people living there who are not on food assistance.
It seems to me that people can get so caught up in dictating what they feel is the optimal use of their tax dollars that it's easy to forget all the real-world complications and other factors that play into the design of food assistance programs.