Minimum wage is simply a constraint that prohibits the creation of some jobs that are available to the most vulnerable members of society in economically depressed regions.

Therefore, making lower-paying jobs illegal just because their salary falls below an arbitrary threshold only stops or hinders those jobs from being created, at the expense of higher unemployment rates.

I'm sure people working on shitty minimum wage jobs would not stay in the same minimum wage job if there were better higher-paying alternatives available to them. If they have no better alternatives than those jobs I don't understand how eliminating them by arbitrarily raising the minimum legal salary limit would leave them better off.