You can
see first hand what happens by looking at large parts of Europe. And the development to push low paid jobs back to the customer themselves does indeed happen, but it happens regardless.
Countries like Norway does not have massive unemployment by international standard, despite one of the flattest salary curves in the world.
> If a business now has to pay someone, say, $10 an hour instead of $7, they will be able to get people with more experience / skill for that price, making it harder for people to get entry-level jobs in the first place.
This assumes the more qualified people want those jobs, even at $10 instead of $7.
If I could get a job as a cleaner for what I make as a software developer, I'd still pick the (much less physically demanding, and less soul destroying) job as a software developer.
If salary was even the main determinant for why people pick the jobs they do, then we'd practically have no nurses or teachers, for example - both jobs that require disproportionally long education for the often very low salaries they command.
Or even law.
In the UK, the average salary for solicitors (who require 3 or 4 years for a degree plus the Legal Practice Course of one year plus two years of practice before you become qualified) is lower than the national average salary.
You can make far more in many professions that don't require even a degree. In fact, there are people in retail and fast food jobs that make more than many UK solicitors, yet work normal hours where many solicitors work hours that are illegal in most European countries.
But most of the positions that are in the territory that would be affected by minimum wage restrictions tends to be positions primarily attracting the totally unqualified that are generally positions that are extremely unattractive for qualified workers and remain so for most even if the salary was better.
How many people do you come across that actively want to make a career for themselves working themselves up the ladder in McDonalds? Yet making manager at a McDonalds in the UK can net you 45k GBP/year or more - far above the average UK salary. Economically, a large proportion of UK solicitors, teachers, nurses and many others would be better off working at McDonalds. Yet we don't see a massive flight of highly qualified people to McDonalds or similar.