Except that has nothing to do with a minimum wage people can actually survive on, and the politics and the politicians aren't the problem.
In this case, those few politicians who want a higher minimum wage are literally trying to help the poorest people in society get a wage that pays for food, clothing and shelter. $15 isn't enough to get them much more than that, not even health care or expensive schools. And last I checked, the politicians were supposed to work for the people.
Automation will replace the burger flippers anyway, it's a mindless simple job a robot can literally do. Instead of paying someone $7 per hour, they'll put in automated ordering kiosks. In fact, if people let themselves be taken advantage of to the point that they'd work for, let's say $1 an hour, they'd still lose the jobs because the automated kiosks will work for nearly $0 an hour.
There are reports out there that robots can take over 38% of all US jobs within 15 years.
So these problems have very little - if anything - to do with the minimum wage.