This is the most salient point in my opinion when discussing minimum wages. Employers have to decide which potential employee can produce enough to make up for the wages that they pay. The higher the minimum wage goes, there are less opportunities to get a career started due to not being hired. Experience is highly valued in almost every field. If you cannot get a low paying job just to build some experience in your resume, you delay or never get the next high paying job. Minimum wage ends up crippling the very people it was meant to help.
With the AI cliff that you discuss, productivity will increase even more than it did in the industrial revolution and there is even less of a reason to continue with our absurd current system of making a tiny out of people rich at the expense of everyone else.
It feels deeply infantilizing to me, and will absolutely cut off the bottom rung of society and hasten the unprepared and unskilled towards the coming AI cliff in my opinion.
I personally did not have my own shit together enough to earn minimum wage, not quite, at the very start. $15/hr+ starts to become a mountain that the least well-off cannot land a position earning, or cannot stay competitive at that rate, in some parts of the nation.