Not really because piecework and off-the-books work exist. Plus in the USA there are entire classes of work for which the normal minimum wage does not apply. I

Not really because piecework and off-the-books work exist. Plus in the USA there are entire classes of work for which the normal minimum wage does not apply. I also doubt that empirical evidence supports that assertion. How many people are really being priced out of work because they are only worth $6/hr, not $7.25/hr? In my experience people on the low end are either worth at least what you're paying them, or they're basically not worth hiring at all, at any wage point, because they disrupt others in the work environment, cause accidents, are not amenable to working in groups nor amenable to working alone, report to work too unreliably to make effective use of, or whatever issue they have that makes them count among the ranks of the "least skilled." Sure, your argument holds given some value of MW, $20/hr? $25/hr? But in real world practice I think the number of people harmed by living out of their car or in shelters @ $7.25/hr vastly exceeds the number of people who but for the minimum wage would easily find relaxing side work at $2/hr sweeping gutters. And in theory the MW could be tailored to mitigate any adverse impact. It could be restricted to employers grossing over $1 million/yr or in excess of 10 employees. It could be augmented with an earned income tax credit, which has been done to considerable success. There could be a separate under-21 MW. Etc. In practice, though, movement seems to be going in the other direction: about half of US states have minimum wages higher than the Federal level, even places like Florida and Missouri which are not liberal strongholds.