It's all about how big the pool of people are who can do the job, and how quickly a new person off the street can take over. If any able-bodied and employable person can do the job and be trained to be productive in a few minutes or hours, that's a low skill job, regardless of how difficult it may be in terms of some physical or emotional metrics.

If I quit my job as an office assistant or research intern, my employer has to do some decent legwork to find someone with the base education and skills that are qualified for that job. I can’t do those jobs if I don’t have college level reading and writing skills or understand basic research practices that are learned in college level courses. And this is just at the lowest intern level of the professions.

The restaurant looking for a server or dishwasher can take anyone with a GED off the street and get them productive in a matter of hours or days. The lowest level restaurant employees (dishwashers and bussers) don’t even need to know how to read.

I agree that minimum wage should be a living wage that ensures a decent life in the context of a country with excessive wealth that is concentrated among the few.

But I think it’s something of a denial of reality to claim that minimum wage jobs aren’t low skill, because they generally are low skill as far as your skill requirements to get a foot in the door. Most of the skills involved are learned within hours or days not weeks or months.

There are high skill jobs that are similarly or more physically difficult than a server or a dishwasher and require long apprenticeships, education, and/or training: jobs like professional sports athletes, deep sea welders, Hollywood stunt professionals, many performing arts jobs like the people backstage at a theater production or the musicians in a touring band.