You could say the same thing about hundreds of businesses in major cities, like NYC, where there almost always lower priced substitute options than higher priced, manual labor intensive options, but due to convenience and marketing they are very profitable. So you are totally neglecting convenience, which is pretty much what fast food operates upon.
Also you neglect that for convenience & marketing reasons people will pay can and will more for the same product & many times lower quality products as well. A perfect example of this would be how much more (as a percentage of their salaries and many times outright) poor people pay for food & transit in urban areas because that is what is offered to them. So while there will be a highly group of tight wads that scour the entire metro area for cheaper options, something like a minimum wage raise is not going to stop people from buying local junk food.
The second part of what you said is just on anecdotal fluff. Living wage tests in Canada have shown that paying people a basic wage doesn't lead to growth stagnation in adults. So the idea that all adults are going to give up on school or academics and flip burgers is just scare tactics as well.