Because in most places, a fast food job is primarily a job one expects to hold for only a few years while getting the education needed to hold a better job that can afford to pay a living wage for a head of household.
The problem is that for many people it's not.
That still leaves the question of whether the minimum wage is the best way to help them. I don't think so. At $15/hour, Target is going to have considerable incentive to find new ways to automate jobs. Might well make it cost effective to place RFID tags on all its merchandise so that all a customer need do for self-checkout is bag the products, swipe their card, and go without having to even bother with the hassle of scanning barcodes.
In the strike mentioned in the OP, at $15/hr, it makes it even more feasible to offshore the drive thru window as is already being done. (There are already restaurants where the person who takes the order at the drive thru isn't even at the restaurant.)
Government benefits as well as a better educational system to help keep people from getting stuck in low wage jobs in the first place are both better responses to the problem than the minimum wage.
Also worth noting -- college education has become fiendishly expensive. Retailers generally disapprove of employees doing anything that would compromise the flexibility of employees' schedules such as taking college-level classes. Industrial labor may have been numbing, but at least with a union contract one could expect some rigidity in a schedule that allowed one to attend college courses.
...I am well aware of some of the techniques in place. Bar-codes have become a substitute for price tags, and a company like Dollar General might have the price printed on boxed objects.