Problem is that the minimum wage can actually work against all of us if the wage isn't properly adjusted for inflation. Otherwise a minimum wage eventually leaves a full time worker living in poverty and requiring medicaid, food stamps, and housing assistance just to get by. It sets an artificial baseline that employers will try to aim for. So if semi-skilled workers get minimum wage, skilled workers get minimum wage plus a bag of peanuts. An artificially low minimum wage drags down wages for all workers except those that assign their own compensation - those executives that sit on each other's boards of directors and, like monkeys grooming each other, mutually decide to keep increasing each others pay regardless of whether the company is profitable or failing. Meanwhile shareholders have been conditioned to expect returns that fall below inflation (when they aren't negative), and workers have grown accustomed to just trying to keep whatever job they have rather than believing they deserve a reasonable share of the profits they produce. The collective fear of the workers makes sure that those few who may have the audacity to make demands can easily be replaced by a more agreeable and subservient employee.
When the minimum wage is a living wage, every worker can have confidence confronting employers about working hours, working conditions, or even ask for more pay, knowing that a worst case scenario is they have to get a job elsewhere that pays a wage that they can manage to live with. Workers higher up on the pay scale can afford to take chances with their careers knowing that in the short term they can always fall back to a lower paying job if their plans don't work out. It's ultimately better for the economy as a whole. Satisfied workers are more productive and less likely to leave, even if the short term cost to employers is to pay more. But as all employers would be paying the same they wouldn't be going out of business from paying better wages.