Exactly. People won't work for less than their worth. So a minimum wage doesn't accomplish much except set a price floor that excludes low value add workers from the economy.
People do it all the time. When their basic needs (food, health, shelter) aren't being met, they'll take whatever work they can. It doesn't mean they're getting their true worth out of that work, it just means they're getting screwed by their employers who are taking advantage of their need to pay them less than they would otherwise.
We need minimum wage laws to protect people from being crunched by capitalists exploiting labor market inefficiencies.
Says who?
Inefficiencies in the labor market happen all the time. A minimum wage is one way to protect desperate people from being unfairly exploited.
That's beyond absurd, showing no understanding at all about human nature whatsoever. I have billions of counterexamples for you. I cannot think of anyone I know who hasn't done this at some time in their life. Working for less than one's worth is, in fact, what the majority of the human race is doing. Working for one's worth or for more than one's worth is what is rare and almost nonexistent.