Sure, that's the premise. The reality is somewhat different. Contracting positions are more flexible (you decide your own benefits) and can be more lucrative if you manage them correctly. They're not for everyone, of course. It's similar to deciding between DIY vs. COTS—the former requires more skill and personal investment but may give better results than the generic store-bought product under the right circumstances.

If you don't want to work a job, contract or otherwise, paying less than some arbitrary "living wage", then don't. No one is forcing you to take the job. You are free to set your own personal minimum wage. But if you think the solution to your woes is to make it so that no one else can take the job either, at least be honest and admit that what you are really trying to do is to improve your own bargaining position by hobbling the competition.

The real complication is that such markets' equilibrium point is hard to shift once it gets stuck in a low wage.

Currently there's a big oversupply of labor, especially for low-wage positions. ( https://economics.mit.edu/files/11563 ) And thus this becomes the classic coordination problem.

While minimum wage is necessarily problematic, because there are many who happen to have some time to earn a bit of extra by doing gigs - which is pretty efficient from a raw economic point of view, but it doesn't help those who are not in it for that bit of extra.

Basically we'd like to change the labor share of income for low wage jobs.

(I think a robust safety net and/or a Negative Income Tax UBI would be much better than direct minimum wage laws.)