The left main thing is mostly about making sure there is a "floor", meaning that even if you are poor and on min wage you don't die on the street or bankrupt at the first opportunity.

Usually, countries where the right is in power (take the US for example) have a terrible living for their poorest population.

And this is not something you want because the guy having the shitty min wage job might tomorrow be you, one of your kids, your best friend, or someone in your family.