Even if the total amount of money in the economy is fixed, the distribution of that money among people matters a great deal to the health of economy which is something your simplistic argument doesn't address.
In the most extreme example if one uber-rich person has almost all of the money and the rest of the country has just enough to buy food, it doesn't matter how much money that uber-rich person has - the economy will be in the shitters because uber-rich person only needs one house, one car, can eat out only in one restaurant per night etc. but if no-one else can afford a car, the cars will not be made (it's too expensive to make just one car).
If there are millions of people that are only one millionth as wealthy as our uber-rich person but wealthy enough to afford a car, a house, a tv set etc., the economy can develop - if there's market for million cars, someone has to be employed to make those cars, tv sets, serve food to those millions of people and a virtuous cycle develops where people employed to create things and services for wealthy people become wealthy themselves.
So the question is: is raising minimum wage creates more over-all wealth (by transferring more money from rich people who have excess of it) or less over-all wealth (by making services of poor people too expensive for rich people).
I don't know what the answer is but you certainly haven't proven that 20% rise of McDonald's prices would cause McDonald's collapse because of massive "I make my own sandwich" movement. Even if that was purely a matter of price (and not, say, convenience of getting a hamburger and fries in few minutes in the middle of San Francisco), McDonald would probably beat you regardless of what minimum wage is due to massive economies of scale, not to mention that making your own sandwich is like using Linux: it's only free if your time is worth nothing.