From a cold market perspective, I would agree with you. But normative economic models must account for social issues in addition to market dynamics. I think it may be very justifiable for governments to impose regulations on certain prices as a means to improve social and economical equity among a society. This is not restricted to minimum wages, but also other variables like weekly work hours and contractual obligations between employers and employees.
I don't think it that the conclusion of decreased labor demand from firms is an immediate conclusion from a rise in the minimum wage. This is an oversimplified look at the complex dynamics of markets at a global scale. As long as there is marginal costs stay below marginal gains, no big shift in demand should occur.
Firms may try to reflect the increase of production costs in the final price of their products, but if these products are no subject to market price regulations, the equilibrium doesn't depend only on the firm's part but also on the buyers' part, who might not be willing to buy at those higher prices. Furthermore, since wages also rise, it might be that purchasing power may increase even if prices rise. Careful models have to be employed to make these calculations. Finally, the rise in labor costs could be supported by cutting some of the profit, which I think is the main point. This would require a great legislative effort to make such regulations fair and effective, but I think it can be done.
Finally, the point about the black market is a mute one, I think. Firms should be audited and punished if illegal activities are detected, whichever the minimum wage is.
Wages are set by how much contribution that person or position is able to bring to the bottom line of the company. Where profit margin is low, wages will also be low. Where the knowledge is minimal to do the work, wages will also be low. Where the service is not in demand wages will also be low. it is the bottom line that counts, why would anyone set up a busy if his intention is not to make a profit, any business contrary to this is called a charity. If a business does not make money to cover its cost then good-bye jobs. However I would agree that CEOs at the top are making an obscene amount of money which is tantamount to theft. Sometimes they are justified and most of the times not.
After all I think of it this way, there are two primary legal entities in the labour market, businesses and people; only one of those entities feels hunger, pain and dis-appointment. I think then extracting which should have ethical priority is not a difficult decision. Businesses have an ethical duty to the society within which they operate, they exist only to benefit people; the concept that businesses occupy a state of having more rights than people is wrong, and they do not exist purely to create profit.