If a job is worth $10/hr to get done, nobody will ever pay anyone $15 to do it. They will just not do it at all - so that’s 10/hr somebody could’ve earned that is just burned.
You have to think of it like that: congressman standing in front of poor single mother, telling her “you’re not allowed to have this job, it’s for your own good”, and then lighting 60% of her desired salary on fire as she looks on in dismay.
Eventually somebody will invent a robot or outsourcing solution that gets the job done for $10/hr.
At no point was any of this ever helpful to that person who was willing to do the job.
So you assert labor demand is completely inflexible. Is this supported by evidence? Perhaps $15 is really too much, I don't know, but to help decide by now we should have hundred year worth of data no?
We should want mothers to have some time and energy left to care for children when they come home. Are there any such $5-$10/hour jobs?
Minimum wage hikes are counterproductive - it’s a ban on jobs for people whose skills are worth less than the minimum wage, which are the poorest people who need the jobs most.
It’s a terrible thing to say to someone - “The best you can do is $6/hr, so we as a society have decided you’re not allowed to work to support or feed yourself.”
But we can make our society more functional to penalise poor people less. The people who can only run a 10 minute mile shouldn’t be forced to do it with a weighted vest. The people who can only run a 15 minute mile shouldn’t be banned from running at all.