And yet it is in Australia, and in slightly better restaurants. If a "burger flipper" is managing/repairing/problem solving several burger flipping machines, then it certainly is a $15/hour job. A burger flipper in Northern Alaska or on an oil platform at sea could definitely be worth $15/hour. In the future, it could be required to be a $15/hour job.
Your absolute statement is wrong. It made more sense when you claimed it did not deserve to be. What someone is paid is dependent on what the market can bare, not on what you think they deserve.
You would rather shutdown a profitable business than pay employees what the market will bare? That is stupid, but it really does not matter. If you shutdown your business, other businesses will take their place, and they will pay employees what the market will bare.
I have people tell me all the time they will not pay my rates. They scream and cry how unfair it is. You know what, NO ONE CARES!!! Capitalism is not about being fair.
You may say minimum wage is not capitalism, but whether you stay in business or not is capitalism. There will be businesses able to pay minimum wage, and if you are unwilling to, they will gladly replace you.
I see you go by the school of thought "consistency is the hobgoblin of little minds." First you said you would never pay anyone over a minimum wage of $15, and now you are saying you would pay all your employees over a minimum wage of $15.
I consider the second strategy to be better. Pay more than the minimum and get the best workers, or at least above average. Let the other guys go with the least employees. They will save a few bucks, but lose so much in quality it will not matter.