Why did Newmans Own cookies (and other products) use “American Gothic” as part of their branding scheme?
Well, I am really no more qualified to answer that than you are. Why do you think so? My best guess is that the painting exemplifies certain values–hard work, respect for the land, rejection of fancy modern technology–that Newman wanted to identify with his products. Plus, dressing up Paul Newman is a little bit amusing, and I suspect he liked that aspect, too. In any case, “American Gothic” is one of the most frequently appropriated and satirized paintings in history (right up there with the “Mona Lisa”). See here and here and here for a few examples.