> it implies that the employee being hired wouldn't be willing to do it for less themselves.

I agree the person who would work for less might even be the person taking the minimum wage job.

I disagree that this decreases class mobility though. Lowered labor costs mean lower barrier of entry to starting your own business. There’s a floor to how much it costs to start a labor dependent business and it’s based on minimum wage. That means you need substantial capital to get started. Also, lower wages means lower prices which disproportionately benefits poor people.