For a family of four, the max benefit would be about $200/week. I feed my middle-class family well, and I doubt I spend much more than that on food, on average. Of course, I buy lots of fresh produce, chicken, meat, and seafood, and we cook it, rather than buying a lot of pre-packaged microwavable crap.
Cooking... real cooking like our grandmothers did... is far, far cheaper than ready-to-eat meals. Also, a lot of money can be saved simply by avoiding waste. Our grandmothers didn't throw a lot of food out. At least mine didn't.
My wife does regularly buy one ready-to-eat thing, though. She gets a rotisserie chicken from Costco. Day one, she has the legs and I have some breast meat. Day two, she picks the chicken clean and makes chicken tacos. Day three, the carcass goes in a stock pot and she makes vegetable soup.
I'm pretty sure that chicken is less than $5, and she gets at least six meals out of it. Good meals, too, and I would classify a rotisserie chicken as "convenience food."
When you factor in things to round it out... rice, beans, fresh vegetables... it's still a healthy stretch of eating on not much money.