Are low-wage workers going to replaced by robots? There are cases to be made for that happening, both here: The Shift From Low-Wage Worker to Robot Worker from FiveThirtyEight and from the recent book, The Second Machine age (pictured above). Indeed, some have argued that fast food restaurants are a form of manufacturing, and this makes the notion of replacing works with machines more plausible to me.
It is important not just to look at the future, but also the past, in particular, the history of the automat.
The automat was once the future too, and there are still vestiges of them around, but mainly they have died off. There were a number of reasons for this (see Automat – Wikipedia, the free encyclopedia), but inflexibility was one of them. Right now fast food establishments thrive on inflexibility and low cost.That is also the way to compete with them. I can see how people can compete with that and win, and the way to do that is portable food (e.g., food trucks, food stalls). Barring bureaucratic costs, portable food is cheaper to deliver than traditional bricks and mortar establishments (even fast food ones). And portable food vendors can be much more flexible than fast food places can ever be.
The other way to compete with them is by being human and offering better service. No robot in the next century will be able to do that.