It's a good idea. I see two problems with it out of the gate:

First, if it isn't accompanied by other changes, it will increase the equilibrium price of food until the poorest are just as squeezed as they are now, or maybe slightly less. "Other changes" could include price caps (perhaps voluntary -- grocery stores which agree to the program must also agree to a set of pricing regulations, and they would agree because it lowers their prices for the public without lowering their profit, meaning they have more customers who buy more), breaking up monopolies, or something drastic like a Crown grocery store chain. There could be other ideas too, but you'd have to do something to avoid it just being a subsidy to grocery giants.

Second, programs which are limited to specific foods often take weird stances about what is "acceptable" for poor people to buy. Not only does this rob them of dignity, it's often very poorly-managed, results in a lot of administrative overhead, and prevents people from buying things like fresh fruit, certain (even cheaper!) brands over others, or food compliant with their dietary restrictions. I'd instead advocate for either no restrictions on what food is purchased, or a blacklist where the card works in every participating grocery store for every product except explicitly excluded ones.