That's false, and dishonest. You seem to have no concept of economics. Prices and the cost of a thing are not determined by the employees need to survive. Price and the cost of a thing are determined by supply, demand, technology, location, and taxation.
The kind of jobs you are referring to are not devalued in an emotional sense, rather an economic one. People do appreciate that some jobs that are necessary have low wages.
Since these jobs require very little training, almost anyone can do them. When the supply is larger than demand the economic value goes down, because Math. If there were no minimum wage requirements the jobs you referenced would be paid even less.
If there is a $15 minimum wage, most unskilled workers will be unemployable. That is $30,000 before taxation and mandatory healthcare. Why pay a person $30,000, when you can replace them with an automated system? And before you say, but people like interacting with people ... remember the kind of jobs you referenced, "cashier, stock boy, and burger flipper". When the board does their cost benefit analysis and weighs $30,000 for unskilled labor vs $30,000 for a robot or automated system that can run forever with minimal maintenance, who will they choose?
Wages will have to increase in kind from the bottom up to account for the shift in how much minimal skilled labor is worth.
We're not there yet, but if the value of skilled labor is further reduced by this push for a $15 minimum wage, we will begin to see an increased pace of automation in service industries.
Many CEOs have already hinted at this, and even more will as political pressures and technology continue their current trends.
You're push to be taken care of with minimal effort will be realized soon, you just won't be working for it.
The State will provide for you by renting automated services from Google, Amazon, and Elon Musk.
Hopefully your UBI checks will cover all the stuff you find to do during your 8 hours of free time every week.
If someone accepts to work at current minimum wage when other opportunities are available that is their decision.
To fix this ... there will be a push to increase minimum education and competence.
There is a bottom for a reason. When you see yourself at the bottom you have to increase your value to rise up, you don't rise up by pulling other people down. Don't devalue other people's work just because your work doesn't have much economic value.