No, it isn't. But neither is $0/hour because you don't have a job, and society doesn't get the product that the $1/hour job produces.
Ideally, the system would pay the workers the marginal value of their input for the work done, and the government would "top up" the wages to whatever the living wage is. Everyone wins. Of course, this is hard to measure and apply.
This is some real galaxy-brain level thinking. Enforcing a minimum wage is a more efficient market.
For the vast majority of the world, outside of ultra-expensive first world metropolises, $15 an hour is beyond a comfortable living wage.
That's largely because the basic necessities of living (housing, clothing, food, transportation) are needed in roughly the same amount by all people, and don't scale with class/income/wealth. I live in a 1-bedroom apartment and eat about three meals a day and wear jeans that cost about $50. I have friends who make an order of magnitude more and less than I do. They don't live in a 10-bedroom or 0.1-bedroom place, respectively. They don't eat 30 or 0.3 meals a day, respectively, and their meal themselves don't cost ten times more or less - maybe there's a factor of two or three. The ones who make ten times more than I do might occasionally buy $500 jeans, but even they won't wear it for everyday use, and the ones who make ten times less generally don't buy $5 jeans either.
So, demand is roughly the same from everyone / doesn't scale very much, and the rich can afford to pay quite a bit more. So a market that has rich people in it will have a higher cost of living.
If you want to stop this, the obvious solution is to prevent income inequality (in all its forms - Paul Graham points out, correctly, that this would require us to rethink the very idea of for-profit unicorns - see https://twitter.com/paulg/status/886953410356011008 and https://twitter.com/paulg/status/645343476662427648). Useful tools include extremely high wealth and income taxes. (And, as someone who by any objective standard makes a lot of money, this is why I'm personally in favor of my own marginal tax bracket being 90% or higher - because it means that people who make even more money than I do can't as trivially outbid me for housing, etc.)
I strongly agree with this, but this requires altruistic employers, or unions to accomplish. And this results in jealousy and hostility towards workers in high-margin industries. Workers in general have no idea what their value-add to the company really is.
Some portion of that marginal value must be retained by the business to pay fixed costs of the business and likely financing costs as well.
The curve that's actually interesting is the expected value to an individual worker of the minimum wage, i.e., the wage multiplied by "how likely am I to be employed fully" (approximately 100% at $1/hour, quite a bit less at $100/hour). Obviously, that curve starts at zero, goes up linearly for a bit, then heads back towards zero in the limit. The question is where "a bit" is and what the argmax is.