Regional mini-burger chain White Castle is experimenting with adding wine to the menu at one Indiana location. This in a way makes sense as small burgers ("sliders") seem to be all the upscale rage these days, making a little pairing seem sensible. But I don't really see this trend taking off. The article notes that the wine-serving White Castle features table service because that's required by state law. And that, it seems to me, is precisely why large fast food chains tend not to offer alcoholic beverages—the relevant regulations vary quite a lot from place to place and are often very burdensome so it makes sense to keep things simple and stay away from the booze.
That said, if booze sales at fast food joints did become more of a regular thing it could upend the industry. At upscale restaurants food is largely a loss-leader for a business that makes its real profits on beverages. Fast food gets some of that with the fountain sodas, of course, but an expanded roster of beverage offerings would drive things further in that direction. Currently the need for food to pay its own freight is one reason there's such a focus on keeping food costs low, which often badly compromises quality.