Kraft Heinz, Maker of Kool-Aid and Jell-O, Thinks Healthy

The company sells some of the most iconic American brands. That may be one of its biggest weaknesses.

Kraft Heinz Co. has a large number of famed brands that are locked into Americans’ memories. Among them: Kool-Aid, Jell-O, Oscar Mayer.

But that strength, in products not typically associated with healthy choices, may now be a weakness, as consumers seek fresher, more natural foods.

A merger three years ago created the food giant, and now...