A reader offers some additional context on whether restricting food stamp purchases is necessary to ensure healthy eating on part of recipients:
On food spending among food stamp participants: there is evidence that food stamp receipt does alter how households spend their money on food. Journal article here and ungated report here.
In short, food stamp participants spend more on at-home food and less on food away from home than comparable non-participant households with the same income. This implies food stamps can not only increase food security but also shift household food spending towards types of food that are subsidized (at-home food, under current rules) AND away from foods that are not subsidized–without making any restrictions on how households spend their own money.
I understand the impulse that drives people to demand restrictions on how food stamp recipients use their assistance, but the simple fact is that it's both wrong and unnecessary.