I'm about as pro-capitalist as they come but I don't see a benefit in removing the minimum wage. All it would mean is a greater need for government assistance for people that hold jobs with ridiculously low salaries.
In capitalism, the lower the wage, the more profitable for the owner - on a small scale at least, ignoring the need for consumers to have money to buy.
The closer to zero, the better, down to the point workers have just enough to eat.
This is the short-term oligarchy - a few people owning huge percentages of a small pie.
But this is how it's usually gone - hence, plenty of 'cheap labor' to build pyramids, or fill armies for conquest or defense, or grow the food for the elite to meet that basic food need.
In Haiti right now, I was just listening to some recent history, all about the minimum wage. Colonies are wanted for up to two things - cheap labor and cheap resources.
For Haiti, it's cheap labor, with a lot of companies setting up factories, paying slave wages/$2 a day.
Their government wanted to raise the minimum wage - which would push neighboring other countries to raise it. Te corporations strongly opposed this, and therefore the US government did.
Aristide was removed, it was said, primarily over the minimum wage, by the first Bush. Years later, Clinton reinstated him with a lot of conditions, one was to not raise the minimum wage.
Then Bush 43 removed him for similar reasons.
There's an army of propagandists against the minmium wage, because powerful people profit from not having one, or lowering it at least.