Consider the lowly cup of coffee, upon which much of the world relies to get going every morning. If you have that cup of coffee at home, you might have bought pre-ground coffee at the store, put it into a machine and drank it out of a cup you then poured into. Or perhaps you used a K-cup. Either way, you had to acquire the coffee (which means either you went out to get it, or someone came to you with it) and you'll have to dispose of the leftovers (ideally by composting, but why get into it). You can see at least some of the labor, altho by no means all of it.
If, instead, you rolled out of bed, dressed and stopped at a Starbucks, Dunkin' Donuts or the break room at work before settling down to put your shoulder into the great wheel of capitalism, somebody else had to do basically all of the same steps; hopefully benefiting from some efficiencies of scale, but also making some tradeoffs (your home brewed cup probably is a washable ceramic; your go cup might not be so re-usable). There is additional labor here associated with a payment which is not present in the home brew up (probably).
Perhaps on a weekend, you would _sit down_ at a restaurant -- maybe a nice place that serves brunch. Someone would come up to your table and ask you if you want coffee, perhaps with the carafe in hand and cups already on the table, but all the same principles apply. And you probably won't pay as you order, as in the previous paragraph, but it will take longer and occur after you are done with your coffee (and brunch).
A lot of restaurant business involves beverages -- coffee or other -- and a lot of that business is automated. We could complete this process (and we probably ought to, when it comes to alcoholic beverages, in the interests of making it possible for the customer to really know what they are getting into, if nothing else) and perhaps it will make sense to do so.
The rest of restaurant business involves food, and while a great deal of that business is standardized (largely because restaurants that do not standardize food have to have amazing markups in order to stay in business and thus constitute a relatively tiny fraction of the restaurant industry albeit with outsize cachet) not so very much of it is mechanized. The mechanical parts involve things like dispensers for consistent amounts of sugar or other sweetener in the coffee, and consistent pours from the soda machine. McDonald's, last I checked, does not automate salting and bagging the fries, despite this, from 2002:
The answer, curiously, may lies in the limits of standardization. (Altho this doesn't actually explain the fry thing.) Momentum Machines burger making robot has a tomato tube and slicer -- I'd love to know what the tolerances are for the tomatoes that go into that tube. I'm betting the ripeness has to be within a very narrow range, and the size must be within narrow limits as well. Food is tough to standardize -- or, rather, standardized food is often unappetizingly tough. And given the difficulty of designing machinery to cope with the relatively wide ranges that many basic food components come in, I suspect the industry has become a bit shy over the years of investing in more attempts. And if the mean time to failure of a complex machine is sufficiently short, it is more reliable to use human labor; the expense and bad feelings caused by each failure only making the calculation in favor of using humans that much clearer.
It's worth noting that the burrito machine I pointed to in a previous post does not allow for any customization -- only whether you add sides or not. It's less clear what the burger robot can or cannot do. But if you stand in line at a McDonald's or Wendy's for any length of time, you'll notice that a lot of the orders are "grill orders" (<- that's McD speak; I don't know what other chains call it), and if you look at their nutrition information online, many of these chains will provide automated menus that let you add and subtract many components of burgers, salads, etc. and recalculate the nutrition information with the change.
How well does a burger robot cope with No Cheese or Hold the Mayo or Extra Pickles or No Onion?
I don't know. But I've spent enough time around robots (I mean this literally) to have a fairly cynical perspective on how effectively they can replace a human. I think we should expect to see more standardization, more front-of-the-house automation, and incremental increases in support equipment (more consistent pours, whether of sweetener, ketchup, mustard, mayo, vodka, wtf). I do not think it is reasonable to expect a dramatic decrease in the number of people working in restaurant kitchens. As each human-hour becomes more efficient through these changes, demand for restaurant kitchen output is likely to increase, particularly if labor in restaurants is simultaneously better compensated (thus making them more able to afford the fruits of their own labor), likely leading, through Jevons paradox, to automation and increased efficiency = increased use.