Equally, if employee Y is producing the same quality of work as employee X but trying to charge more money, does employee Y not deserve to be out-competed by employee X?
Employment is a two-sided market too.
Nobody would advocate for a minimum price for a packet of crisps just to save the poor crisp companies from earning too little per packet. It is obvious that if crisps were too expensive, people would stop buying them. The same applies for workers.
Minimum wage is just saying "if you can't produce at least $X of value per hour, you're not allowed to work at all". That's not fair.
But in a modern democracy, labour has a different sort of power and I cannot think of a moral principle that says that labour should not distort the market using its power at the ballot box.
If a pro-unregulated market candidate can't win more votes than the guy who wants to support minimum wages, he doesn't deserve to win. And he doesn't deserve to enact his policies.
So an ancap can argue his point but if he can't win in the marketplace of ideas, then he doesn't win. Because that market is truly free.
That's fair.