What your econ 101 analysis ignores is that wages are very often not determined by productivity or the value they are generating for the employer, but by bargai

What your econ 101 analysis ignores is that wages are very often not determined by productivity or the value they are generating for the employer, but by bargaining power. This is particularly so at the low end of the labor market. In the real world, there's plenty of evidence that minimum wages have a positive influence of employment, wellbeing, and allocative efficiency. To the extent that they eliminate jobs in truly low-productivity sectors, that's actually a good thing, as those people can be moved into higher productivity sectors - you just need a welfare state that handles the income instability and retraining costs for those involved.