Walking into some quick-service restaurants these days can make you feel like you’ve just wandered into the produce section at Whole Foods. A colorful cornucopia of fresh fruit—from deep-yellow mangos and light-green apples to purple pomegranates and ruby-red strawberries—is getting highlighted in every menu category. Fruits from across the world are showing up in breakfast items, as part of eye-catching salads, as accompanying elements to entrees, as fresh-pressed beverages, and as healthy dessert options. This fruit usually travels a long and complex road from the orchards, fields, and groves to a quick-service chain’s multiple outlets. Ensuring that consumers get a fresh product can be difficult, so...