I don't think your analysis is correct. Due to the imbalance of workers to jobs a price control in appropriate. I think it should be set locally not nationally but a national minimum is not unreasonable.

If a higher minimum wage leads to automation that is not a bug it is a feature. People should not be expected to do work that is better automated. Prior to the pandemic unemployment was very low.

Wage Slave labor is just as evil as child labor.

TEK