That is absolutely true, but not because of the mayo. An hour is a short time, but these are often picnic foods left outside in hot weather for more than hour. The mayo is a pile of oil with very little egg in, and the egg is dispersed through the oil and not exposed to the air. Many of the other contents of the salads can spoil in the heat though. Then people think the food went bad because of the mayo and the cycle of explanations starts again.
Right. Mayo by itself will keep at room temperature indefinitely. But when you mix it with other ingredients like chicken or potatoes, it dilutes the acidity. They will have had bacteria on them that can grow.
That sort of thing happens in Japan itself, too. I’ve never been there, but reviews at soranews24.com often mention items limited to x items per day, and it is a pretty common trope in anime and manga for someone to rush to get in line for some limited food item. That has always seemed weird to me for a business to limit to a small amount of items per day where they know demand outstrips supply. Not expanding supply is just throwing away money.
I hate this kind of sensationalism.
They are just meatballs - way, way more than they are burgers. Or better yet - a kind of sausage, IMO. And no bun is mentioned in De re coquinaria, which IMO definitely makes them not a burger.
I’ve made them, they’re lovely. Mine were shaped like crépinette.
Hear me out here: maybe, just maybe, quality of life trumps money for these cooks.
And keep them wanting more is a way to lure them back without making your product a common commodity.
And what is it that makes you assume that the item limited to 20 or 50 (or whatever) a day is that much harder to produce than the rest of the daily stock?
Nothing. I make no such assumption.
But making more of a thing, when done artisinally, must necessarily mean taking more time to make it. Time the cook may not want to spend.
Example: I have “X” amount of smoker space. That means the amount of brisket I can turn out any given day is limited. The choices are either accept that fact and turn away customers when the meat is gone, or dilute the product by expanding beyond what I am capable of doing comfortably. Easy choice, and people can just get here earlier. See Franklin BBQ.
Economies of scale. If you run out of the food you prepared early in the morning, it doesn’t make sense to whip up a new batch in midafternoon. A lot of it will probably go to waste at the end of the day.
Different concept and execution.
Limited products are popular in Japan probably because of the sense of exclusivity. There’s a Japanese bakery near me that has Japanese/French pigs in the blanket (two small sausages wrapped in a croissant) that’s limited to 40 a day. I’ve had it a couple of times and don’t find anything special about it.
As discussed in the article I linked to, okazuyas grew out of the demand for field workers to make their their own bento (lunch) box to be eaten at lunch. The concept works for the business makes since after the lunch hour, the traffic and demand dies. I’ve never known anyone visiting an okazuya to keep the food for dinner. At most, dinner is leftovers from lunch.
Could they close and reopen for dinner? Possibly, but most okazuya have limited or no seating. Some of them are just a window open to the street. I think most people think of dinner as a hot or cold meal (salad and sandwich?), not room temp.
Another thing is that the larger okazuyas main business is catering. So the take out business may be a side of their preparing much larger orders. Most will close for the day if they have large catering orders.
“And what is it that makes you assume that the item limited to 20 or 50 (or whatever) a day is that much harder to produce than the rest of the daily stock?”
I know that there are “purist” chefs/cooks around the world, but I’ve seen a lot of shows about Japanese chefs/cooks who choose to limit their output to maintain quality.
One restaurant that stands out in my mind was shown on Soko Ga Shiratai a 70’s Japanese show that covered numerous topics. This one was about limited food items.
The dish was a single slice of pork belly simmered for hours only in soy sauce. What made this dish so special was it that the chef would buy a section of pork belly, after very critical selection, then cut a limited number of slices (I think 5-6) from the center of the belly which he considered the best. Rinse and repeat the next day.
Then there are “food artists” that have grown older without anyone willing to take over their craft. They can only produce a limited number of their product because of age. Once they’re gone, the taste will go with them.
I don’t know how closely this matches your requirements, but in the ancient Near East prepared foods from offerings to the gods were distributed to various people. Wages also took the form of prepared foods as well as food ingredients and other items.
I agree that cooking on demand for customers, and stocking enough ingredients that you could expect not to sell out of food before you’d run out of customers, seems likely to have been a later development than selling a fixed supply of prepared food. Preparing food on your sale premises requires fuel, workspace, ability to transport and store large amounts of ingredients, etc. All of these would likely have been at a premium in, e.g., a marketplace of 3rd-millennium BCE Sumer.
Good thing I pointed to an article that does describe them as an evolutionary step towards the hamburger. But not here to argue about the shape, the main reason for the post was to show that “‘fast food joints’ – or thermopolia as they called them –” were brought by the Romans to Britain too.
Tell that to the headline of the article, and the text of your own link. “seem to have invented” and “how Romans invented…” are the sensationalism I was talking about. You pointing out that that’s just clickbait doesn’t negate that.
Seems that you are missing that “seems” and “apparently”. 
as noted, not a big deal, and still unrelated to the main point.
No, I didn’t miss the weasel words, they’re pretty much SOP for that kind of clickbait.
Seems to me that you are ignoring that I’m not contradicting you. As this is about what the ancients did regarding how fast food was prepared or preserved for the day or few days they could manage before refrigeration; we can seemingly 
disagree on the shape of the meatball, but what it is fascinating to me is then how that was made in ancient times, I think most would like to see cites about what was done then, regardless of its shape.
I’m not disagreeing about the shape, I’m disagreeing about what makes a burger. If your definition of burger is “any old minced meat” then yeah, it’s a burger. To me, though, there’s a whole lot of stuff that fit that description that are not burger, and shoehorning the isicia into “burger” is mistaken.
There’s a whole separate category of modern food that is “meat wrapped in omentum” that it fits in perfectly. That’s way more interesting historical food trivia than “Roman burger”, and has the added advantages of
a) introducing some people to some current foodways they may not know about
b) being true.
And the point is that that is what the posts should concentrate IMHO. The cite did mention Caul fat, and that is omentum, the thing is that that was going to be my next post but something distracted me. 
It is indeed more fascinating to me that even a dismissed article gets items that are related to the matter at hand. So it was not just a peculiar type of fat, but used as a wrapping.
Now, the question is if the cooking method melted the Omentum or if the ancient Romans did prepare the meatball/patty more like a sausage.