If the market is competitive, then the employer listing a subpar minimum pay will either get subpar candidates or be forced to raise it to compete with their competitors.
These mechanisms are not expected to work over the course of months or even a year. It can take multiple years for the supply curves to move.
(To be clear, that is saying it would be better if raising the minimum wage did increase unemployment, because that would likely indicate the labor market wasn't completely fucked in employees favor to begin with. We simply wouldn't have a minimum wage in that case because there would be enough organic worker power.)
Still, I rather have the transparency. Wide bands for all jobs makes it plainly obvious who holds the power, and that is still useful. Do not want my coworkers to be blissfully ignorant.)