A common argument for banning sweatshop labor asserts that no one should be forced to work in a sweatshop due to economic necessity. Everyone is entitled to a good job.
A standard reply to this argument emphasizes that a ban on sweatshop labor merely takes away options from people who already lack options. Indeed, presumably the reason why someone would decide to work in a sweatshop is precisely because they lack a better option. Of course, if a ban were paired with cash transfers or a guarantee of a good job, that would be a different story. But on its own, a ban harms those it purports to help by taking away their “best bad” option.
If you’re inclined to reject this style of argument, ask yourself if you’d also reject it in parallel cases. Suppose someone argued in favor of banning warming shelters on the grounds that everyone is entitled to decent permanent housing and thus no one should have to make use of a temporary warming shelter. I suspect that very few people would find this argument compelling. Simply banning warming shelters wouldn’t place people in decent permanent housing and would in fact worsen the condition of those in need of shelter.
Of course, we should work towards the goal of creating conditions that enable everyone to enjoy a good job and good housing. But in the meantime, we shouldn’t take away an option from people who already lack good options.
Does the same argument apply ceteris paribus to minimum wage regulations or is there any relevant difference? "If people want to get paid very little to work very hard, then why shouldn't the state let them?" seemingly works for both sweatshops and low wages more in general ("low" depending on context, since minimum wage regulations often extend also to job settings that wouldn't classify as sweatshops).