The problem is that people don't understand that it's a market that determines wages, and instead think it's a number that employers just come up with off the cuff and minimum wage is the only thing stopping them from picking $1/hr.
Right. They also fail to understand that many low end jobs only provide very marginal value to companies and could easily be eliminated if the minimum wage exceeds that value. For instance, baggers at grocery stores hired as a convienence to shoppers and to speed up checkouts. But this is only very marginal value; customers and cashiers can do the bagging themselves and the negative side of that is only very slight to the business. It's an easy job to eliminate first, many stores these days don't have one. Low minimum wages create more jobs like this, which are good jobs for teenagers or people with intellectual disabilities.
Lowering the minimum wage for people with disabilities creates more jobs for people with disabilities, demonstrating the whole point. Higher minimum wage price less capable labor out of jobs.
Don't you think it's a little unlikely that people, in this day and age, with the current political climate in the west, don't "understand that it's a market". I think it's extremely unlikely.
I think it's more likely (because that's what I'm doing, and I expect others to do the same) that we are rejecting your market based framing, because it unnecessarily restricts good political action. I understand that wage can be viewed through the lens of the labor market, even Karl Marx knew that. I just don't think that's a very important or useful lens to view it through.
It's much like viewing political climate action, or product safety action, through the lens of the "market". You can do it, it's just not very useful for setting public policy.
The "labor market" didn't get children out of the factories, restrictions on that market did.