Arguments in favour of a minimum wage mostly hang on the idea that firms have a responsibility to ensure that their workers earn enough to live on. If a firm can’t pay its workers enough to live on, then it isn’t a viable business, because it is dependent on wage subsidies. Of course “enough to live on” depends where you live: the cost of living in London is considerably higher than it is in, say, Newcastle, so a minimum wage that would give a reasonable standard of living in Newcastle is starvation level in London. The campaign for a voluntary Living Wage tries to persuade firms to pay above the current UK minimum wage, which is perceived as being below the real cost of living.
If it did not, child labor, for example could be paid just enough to provide food but no shelter or shelter but no food. The poverty line would know no bottom.
By today's standards this period in the US wasn't very democratic, since minorities and women and poor people could not vote. It became less equal because of wealth disparities.